Calibrating and Completing the Volatility Cube in the SABR Model

G. Dimitroff, J. de Kock Calibrating and completing the volatility cube in the SABR Model

Berichte des Fraunhofer ITWM, Nr. 202 (2011) © Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM 2011

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Bericht 202 (2011)

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Calibrating and Completing the Volatility Cube in the SABR Model

Georgi Dimitroﬀ Johan de Kock

This report describes the calibration and completion of the volatility cube in the SABR model. The description is based on a project done for Assenagon GmbH in Munich. However, we use ﬁctitious market data which resembles realistic market data. The problem posed by our client is formulated in section 1. Here we also motivate why this is a relevant problem. The SABR model is brieﬂy reviewed in section 2. Section 3 discusses the calibration and completion of the volatility cube. An example is presented in section 4. We conclude by suggesting possible future research in section 5.

1 Formulation of the Problem

We first review the interest rate market setup before we formulate the problem solved. European options (calls and puts), being the most basic and liquidly traded contracts, are the building blocks in the equity world. Central concepts like implied volatility are defined with respect to equity options and the Black-Scholes formula for pricing these options. The prices of European puts and calls are frequently quoted as implied volatilities, obtained by inverting the Black-Scholes formula. Due to their liquidity, the prices of these options are available on the market. This is the reason why pricing models for exotic (illiquid) products are usually calibrated in such a way that these liquid calls and puts are priced consistently. The interest rate world (or fixed income world), on the other hand, is characterized by a large number of diverse products. However, interest rate caps, interest rate floors and swaptions can (to a certain extent) be regarded as the equivalent of Europeans options in the interest rate world (see Brigo and Mercurio [2]). These are the most liquid and nonlinear products in the interest rate world and interest rate models are calibrated to consistenly price these instruments. In this report we focus on the swaption market. We now consider swaptions more closely. Let Tm be the option maturity and Tm+1 < Tm+2 < ··· < Tn the payment dates of the swaption, where m, n ∈ N. Thus, Tn − Tm is the swaption tenor and Tn the total maturity. A swaption with maturity Tm and tenor Tn−Tm is a contract allowing the holder to enter an interest rate swap with maturity Tn at time Tm. Such a swaption is usually referred to as a Tm (Tn − Tm) swaption. The fixed leg is equal to the strike K. The swaption is essentially a European call on the underlying interest rate swap. We assume that the payment dates are (taking the day count convention into account) equidistant, ie Ti − Ti−1 = ∆t for i = m + 1, . . . , n.

1 The payoﬀ of the swaption at time Tm is (see Filipovi´c[3])

n + X N[r(Tm) − K] ∆t P (Tm,Ti), i=m+1 where N is the notional, r(Tm) is the swap rate at time Tm and P (t, T ) is the value (at time t) of a zero-coupon bond with maturity T . It is evident + that the price of the swaption is the expectation of [r(Tm) − K] . Therefore, the swaption can be interpreted as a European call on the underlying swap rate r(Tm). The fair forward swap rate at time t is (see Brigo and and Mercurio [2], for example)

P (t, Tm) − P (t, Tn) Smn(t) = Pn . ∆t i=m+1 P (t, Ti) Swaptions are usually priced with the interest rate equivalent of the Black- Scholes formula, namely the Black1 formula (see Black [1]). The swaption volatility, defined with respect to the Black formula, is a central quantity in the interest rate world. Similar to the implied volatility in the equity world, the price of a swaption is frequently quoted in terms of the implied swaption volatility for the underlying swap rate. 2 Denote the implied swaption volatility for a Tm (Tn − Tm) swaption with strike K by σbmn(K). Thus the volatility is a function of the option maturity, tenor and strike. It has become common practice to order the implied swaption volatilities in a three-dimensional structure known as a volatility cube. The x-, y- and z-dimension of the volatility cube are option maturity, tenor and strike respectively. Each point of the cube is the implied volatility for these three values, ie σbmn(K) for Tm, Tn − Tm and K. One does not generally obtain a complete cube from the market. Typically one would have all the volatilities for the at-the-money (ATM) strike values. Therefore, the plane σbmn(KATM) would be complete for all typical values of Tm and Tn − Tm, where KATM is the ATM strike. However, for other strike values K only some market quotes of σbmn(K) would be available. Completing the volatility cube entails “determining” the missing values of σbmn(K). An intuitive approach would be to interpolate between the known values. This would not work well in cases where few values are available, which is frequently the case (see the discussion in section 3 and the example in section 4). The aim of this project is to complete the volatility cube. The first decision to be made is how to model the forward swap rate. The most important requirement on the model is that it captures the market smile and the market skew. This is particularly important in the case of cube completion for two reasons. The first reason is that the available volatility data contains smiles and skews. The second reason is that the (missing) values needed to complete the cube must also exhibit smiles and skews in order to be consistent with the given data, ie the neighboring points.

1Additional to its use in the interest rate world, the Black formula is also used extensively in the foreign exchange (FX) and commodity worlds. 2Note that although the implied swaption volatility is deﬁned in the context of the Black model, an implied volatility can also be extracted when a diﬀerent model is used (as in the equity world). Consequently, the implied swaption volatility is the volatility which, when substituted into the Black formula yields the swaption price given by the chosen model.

2 Given the above-mentioned reasons, a stochastic volatility model seems to be best-suited for modeling the forward swap rate. Such a model takes account of smiles and skews. Furthermore, there is empirical evidence that the swaption volatility is stochastic (see Brigo and Mercurio [2], for example). An important example of a stochastic volatility model is the stochastic volatility enhancement of the popular BGM model3 (see Wu and Zhang [10], for example). Brigo and Mercurio [2] list and cover several stochastic volatility models for the interest rate world. However, our client, Assenagon GmbH, wanted the SABR stochastic volatility model. The next section discusses this model. Before we proceed to present the SABR model, we shortly discuss the practical relevance of the cube completion problem. Why should traders be that interested in having a complete volatility cube? There are two main answers to this question. The ﬁrst answer is that a complete cube contains valuable information on the current state of the market. A completed cube enables traders to consistently quote swaptions diﬀerent from the liquidly traded ones. The second answer is of a practical nature: most commercial interest rate software and modeling tools require a complete cube as input data. Using this cube allows us to price more exotic interest rate derivatives.

2 The SABR Model

The SABR4 model by Hagan, Kumar, Lesniewski and Woodward [5] (see also Hagan and Lesniewski [6] and Hagan, Lesniewski and Woodward [7]) involves the modeling of the forward swap rate Smn(t). The forward swap rate in the SABR model is assumed to evolve according to the stochastic diﬀerential equation (SDE)

βmn dSmn(t) = Vmn(t)(Smn(t)) dWmn(t), (1) where the stochastic volatility is modeled by the driftless SDE

dVmn(t) = σmnVmn(t)dZmn(t). (2)

The initial volatility is

0 Vmn(0) = vmn. (3)

The correlation between the Wiener processes Wmn(t) and Zmn(t) is denoted by ρmn. The correlations between Wiener processes corresponding to diﬀerent maturity-tenor pairs are not relevant for the completion of the cube. Therefore, we can consider Smn(t) and Vmn(t) in isolation. In order to complete the volatility cube, we need an expression for the implied swaption volatility σbmn(K) in the SABR model. The remainder of this section is devoted to the derivation of an expression for σbmn(K). The ﬁrst step in doing this is the derivation of an expression for the option price in the SABR model.

3This model is also known as the LIBOR market model. 4SABR stands for Stochastic, Alpha, Beta and Rho (see Brigo and Mercurio [2]). 0 Note that the value vmn in (3) is frequently denoted by α.

3 The second step is setting this option price equal to the option price in the Black model and thus obtaining the implied volatility. We only perform the first step and refer the reader to Hagan, Kumar, Lesniewski and Woodward [5] for the second step. The first step can again be divided into two parts. The first part is the derivation of a partial differential equation (PDE) for the call price. We do this in somewhat more detail than in [5]. However, the second part of the first step (solving the resulting PDE) is quite technical and not needed for the remainder of our analysis. Thus, we also refer the interested reader to Hagan, Kumar, Lesniewski and Woodward [5] for the solution of this PDE (8). We now derive an expression for the price (at time t) of a European call C(t, T, S, V ) with maturity T . S is the forward rate at time t and V is the volatility at time t. This is a call on the forward swap rate. As mentioned in section 1, it is market practice to price a swaption with a formula similar to Black’s formula (see Brigo and Mercurio [2]). Therefore, the price of a call on the forward swap rate corresponds to the price of a payer swaption. The derivation is based on perturbation theory and our approach is similar to that of Hagan, Kumar, Lesniewski and Woodward [5]. We omit the indices m and n to simplify notation and write the SABR SDEs as

β dSt = VtSt dWt and

dVt = σVtdZt.

The correlation between the Wiener processes Wt and Zt is denoted by ρ. We use the perturbation parameter ε and deﬁne σ σ := e ε and

Vt Vet := . ε The SDEs now become

β dSt = εVetSt dWt and

dVet = εσeVetdZt.

We rewrite these SDEs in terms of independent Wiener processes Wct and Zbt as

β dSt = εVetSt dWct (4) and p 2 dVet = εσeVet ρdWct + 1 − ρ dZbt . (5)

4 Let the transition probability density function be γ, then

γ(u, w, x1, x2, y1, y2)dy1dy2 =

P y1 < Sw < y1 + dy1, y2 < Vew < y2 + dy2 Su = x1, Veu = x2 , where u ≤ w. γ satisﬁes the forward Kolmogorov equation (see Karartzas and Shreve [8], for example)

2 ∂ 1 ∂ h 2 2β 2 i γ(u, w, x1, x2, y1, y2) = 2 ε y1 y2γ(u, w, x1, x2, y1, y2) + ∂w 2 ∂y1 2 1 ∂ 2 2 2 2 ε σe y2γ(u, w, x1, x2, y1, y2) + 2 ∂y2 2 ∂ h 2 β 2 i ε σye 1 y2ργ(u, w, x1, x2, y1, y2) ∂y1∂y2 2 1 2 2 ∂ h 2β i = ε y2 2 y1 γ(u, w, x1, x2, y1, y2) + 2 ∂y1 2 1 2 2 ∂ 2 ε σe 2 y2γ(u, w, x1, x2, y1, y2) + 2 ∂y2 2 2 ∂ h β 2 i ε σρe y1 y2γ(u, w, x1, x2, y1, y2) , (6) ∂y1∂y2 where we have used (4) and (5). We now turn to the call price, which is given by + C(t, T, S, Ve) = E [ST − K] St = S, Vet = Ve Z ∞ Z ∞ = (y1 − K)γ(t, T, S, Ve , y1, y2)dy1dy2 −∞ K = [S − K]++ Z ∞ Z ∞ Z T ∂ (y1 − K) γ(t, w, S, Ve , y1, y2)dwdy1dy2, −∞ K t ∂w where we have used the fact that5 Z w ∂ γ(u, w, x1, x2, y1, y2) = δ(y1 − x1)δ(y2 − x2) + γ(u, s, x1, x2, y1, y2)ds. u ∂s However, since

Z ∞ 2 ∂ 2 0 = 2 y2γ(u, w, x1, x2, y1, y2) dy2 −∞ ∂y2 and

Z ∞ 2 ∂ h β 2 i 0 = y1 y2γ(u, w, x1, x2, y1, y2) dy2 −∞ ∂y1∂y2

5 (see Wu [11] or note that γ vanishes at inﬁnity) we obtain

C(t, T, S, Ve) = [S − K]++

Z ∞ Z ∞ Z T 2 1 2 2 ∂ h 2β i ε (y1 − K)y2 2 y1 γ(t, w, S, Ve , y1, y2) dwdy1dy2 2 −∞ K t ∂y1 by substituting (6) into the equation for the call price. Furthermore, integration by parts yields

Z ∞ 2 2 2β 2 ∂ h 2β i y2K γ(u, w, x1, x2, K, y2) = y2(y1 − K) 2 y1 γ(u, w, x1, x2, y1, y2) dy1. K ∂y1 Therefore, the call price is given by

C(t, T, S, Ve) = [S − K]++ Z ∞ Z T 1 2 2β 2 ε K y2γ(t, w, S, Ve , K, y2)dwdy2, 2 −∞ t where we have changed the order of integration. Let Z ∞ 2 Γ(u, w, x1, x2) := y2γ(u, w, x1, x2, K, y2)dy2 −∞ 2 = E Vew | Su = x1,... , where u ≤ w, then the call price can be expressed as

1 Z T C(t, T, S, Ve) = [S − K]+ + ε2K2β Γ(t, w, S, Ve)dw, (7) 2 t where we have again changed the order of integration. Γ satisﬁes the Feynman- Kac formula (see Karartzas and Shreve [8], for example)

2 ∂ 1 2 2β 2 ∂ − Γ(u, t, x1, x2) = ε x1 x2 2 Γ(u, t, x1, x2)+ ∂u 2 ∂x1 2 1 2 2 2 ∂ ε σe x2 2 Γ(u, t, x1, x2)+ 2 ∂x2 2 2 β 2 ∂ ε σρxe 1 x2 Γ(u, t, x1, x2) (8) ∂x1∂x2 with the boundary condition

2 Γ(t, t, x1, x2) = x2δ(x1 − K). We omit the detail of solving this PDE since the solution steps are quite technical and do not contribute to understanding the model. See Hagan, Kumar, Lesniewski and Woodward [5] for the solution details. Substituting the solution of (8) into (7), one obtains Z ∞ + |S − K| − 3 −q C(t, T, S, Ve) = [S − K] + √ q 2 e dq, 4 π a

6 where

1−β 1−β S − K β a := − ln (KS) 2 − ln b− (S − K)(1 − β) 1 d ε2ρVeσc + . 4 e 2T

The expressions for b, c and d are quite involved and since they are not directly needed in the remainder of this report, we refer the reader to Hagan, Kumar, Lesniewski and Woodward [5]. Using the same technique to derive the option price in the Black setup, one can equate the call prices in the two models (SABR and Black) to obtain an approximate expression for σe. Re-introducing the indices m and n and stressing the strike-dependence K, one obtains the formula

" #−1 (1 − β)2 S (0)2 (1 − β)4 S (0)4 σ (K) ≈ v0 1 + ln mn + ln mn · bmn mn 24 K 1920 K

( " 2 0 2 1−β z (1 − β) v − 2 mn (Smn(0)K) 1 + 1−β + x(z) 24 (Smn(0)K) 0 2 # ) ρmnβmnσmnvmn 2 2 − 3ρmn 1−β + σmn Tm , (9) 2 24 4 (Smn(0)K) where

σ 1−β S (0) mn 2 mn z := 0 (Smn(0)K) ln vmn K and

p1 − 2ρ z + z2 + z − ρ x(z) := ln mn mn . 1 − ρmn Note that only terms of order O(ε2) have been included. Furthermore, ε was set to one to recover Vt and σ from Vet and σe. The formula above is the version found in Mercurio and Pallavicini [9]. Although (9) is an approximate formula, we shall ignore the approximate sign and consider the expression on the right-hand side of (9) as the implied volatility. In order to distinguish between the model implied volatility σbmn(K) and the market-quoted implied volatility, we shall denote the latter by σemn(K) (not to be confused with the perturbation volatility σe without indices).

3 Calibrating the Model and Completing the Cube

The aim of this project is to complete the volatility cube. As pointed out in section 1, the x-, y- and z-dimension of the volatility cube are option maturity,

5δ denotes the Dirac delta.

7 tenor and strike respectively. Each point of the cube is the implied volatility for these three values, ie σbmn(K) (from equation (9)) for Tm, Tn − Tm and K in the case of the SABR model. As pointed out in section 1, one generally only has a complete σbmn(KATM)-plane for all typical values of Tm and Tn −Tm. One reason why one cannot simply interpolate between the given volatility values to find the missing ones, is the sparseness of the given cube. For many strike values K there are so few points σbmn(K) known that it defeats the concept of interpolation. A second reason is the nonlinear structure. For fixed values of m and n, the mapping K 7→ σbmn(K) is anything but flat. It is rather parabolic. This is known as the volatility smile. One can also view it on a surface level. Each plane σbmn(K) (where K remains fixed) can be mapped onto a volatility surface6. The x- and y-dimension of the surface are the option maturity and tenor respectively. The z-dimension is the value σbmn(K). The volatility surface is usually far from being flat. The modeling of the volatility surface is an active area of research and there are entire books (see Gatheral [4], for example) devoted to this topic. The volatility surface is basically a “landscape” with mountains and valleys. Therefore, interpolation will (in most cases) deliver bad results. Knowing only a few points of this landscape, it is impossible to deduce exactly where the mountains and valleys start and end or how high the mountains are and how low the valleys are. Consequently, interpolation makes no sense at all. Therefore, we have decided to calibrate an entire SABR model for each pair (m, n) corresponding to fixed values of Tm and Tn − Tm and all values of K. In the landscape analogy this means that we fix the x- and y-coordinates of a point and calibrate its “height” in all the landscapes simultaneously. It is evident from the SABR model description (1), (2) and (3), that four parameters need to be calibrated. Hagan and Lesniewski [6] suggest fixing one of the parameters ρmn (or βmn) and calibrating the remaining three parameters 0 σmn, vmn and βmn (or ρmn). We have experimented with this approach and obtained the best results when βnm was fixed at 0.5. The first step is to determine the pair (m, n) with the largest number of market-quoted volatilities. That is the swaption with option maturity Tm and tenor Tn − Tm for which σemn(K) is available for the largest number of different 0 0 0 strikes K. Once this pair (m , n ) has been found, σm0n0 , vm0n0 and ρm0n0 are calibrated by means of the least-squares method7. The second step is to calibrate the entire maturity-tenor grid, keeping the maturity fixed and calibrating for each tenor. For each maturity we start by calibrating the tenor with the largest number of quoted volatilities. The starting 0 values of σmn, vmn and ρmn for each pair (m, n) are the values calibrated for 0 the previous pair. The values σm0n0 , vm0n0 and ρm0n0 are used for calibrating the very first pair. A smoothness parameter is applied to the calibration of each pair (m, n) for which few quotes are available. These are typically the pairs for which we only have ATM market volatilities. The smoothness parameter prevents the calibrated parameters from moving too far away from the initial values. We have also implemented a second approach which differs from the ap-

6This volatility surface is not the same as the volatility surface in the equity world where the x- and y-dimension of the surface are the strike and maturity. 7This implies that the volatilies calculated using (9) are ﬁtted to the market volatilities σemn(K).

8 proach above in the calibration of the pairs (m, n) for which several market quotes are available. The parameters for such a pair are calibrated several times. Thus, we calibrate the parameters and then calibrate again using the current values as the starting values.

4 Example

We now apply the procedure from section 3 to ﬁctituous data resembling actual market data from September 2010. The payment frequency is quarterly, ie ∆t = 0.25. Figure 1 is a plot the ATM (ﬁctituous) market volatility surface. The z-dimension is the volatility in percentage. We have the complete ATM volatility surface, which is frequently the case.

50 40 30 20 10

30y

1m Tenor Option Maturity 20y 1y

Figure 1: The Market ATM Volatility Surface

We calibrate the data using the second approach described in section 3. Fig- ure 2 is a plot of the ATM volatility surface resulting from our cube completion. As mentioned in section 3, we fix a point (m, n) and calibrate the SABR model on all strikes simultaneously. Thus, after having considered every point (m, n) all volatility surfaces have been calibrated. Therefore, the ATM volatility surface (which we also have as input data) is a “by-product” of the calibration procedure. Since we know what it should look like (figure 1), the calibrated ATM surface is a good test of our calibration ansatz. Comparing figures 1 and 2, one observes that the two surfaces are almost identical. We can conclude that our calibration procedure can fit the ATM volatilities very accurately. We now turn to one of the volatility surfaces for which we have very few

9 50 40 30 20 10

30y

1m Tenor Option Maturity 20y 1y

Figure 2: The Calibrated ATM Volatility Surface points (volatility values). Figure 3 is a plot of the completed volatility surface (produced by our method) for a strike which is 25 basis points from the ATM strike. Although the shape is plausible, this surface is not as smooth as the ATM surface in ﬁgure 2. The reason for this is that our client wanted a completed volatility cube to use as the input to existing valuation software. The accuracy of the volatility values is more important than the smoothness of the surface in this case. A smoother surface be obtained by using stricter smoothing parameters.

5 Conclusion

The method described in this report has been implemented in Matlab.A corresponding Excel sheet, which communicates with Matlab via the ExLink add-in, has also been created. An important trade-off in the implementation is between the smoothness of the resulting volatility surfaces and the accuracy of the calibration. Accuracy in this context refers to the extent to which the known volatilities are matched by the calibrated surfaces. We have mainly stressed the quality in the example of section 4. An interesting area of future research might be determining an optimal trade-off between smoothness and accuracy. An important advantage of this approach is that the produced volatility surface is free of arbitrage for fixed tenor and maturity. This means that for each volatility curve (m, n), the mapping K 7→ σbmn(K) is arbitrage-free and therefore traders can safely quote prices along this curve. The input values we have used in the example were arbritrage-free. However, frequently market data

10 60 50 40 30 20 10

30y

1m Tenor Option Maturity 20y 1y

Figure 3: The Calibrated Volatility Surface (Strike = 25 bps) contains arbitrage. Another interesting area for future research is exploring arbitrage opportu- nities accross maturities and tenors in order to implement restrictions on the model which result in a completely arbitrage-free cube.

11 References

[1] F Black. The Pricing of Commodity Contracts. Journal of Financial Eco- nomics, 3:167–179, 1976. [2] D Brigo and F Mercurio. Interest Rate Models – Theory and Practice: With Smile, Inﬂation and Credit. Springer-Verlag, Berlin, 2006. [3] D Filipovi´c. Term-Structure Models – A Graduate Course. Springer-Verlag, Berlin, 2009. [4] J Gatheral. The Volatility Surface. John Wiley & Sons, Hoboken, New Jersey, 2006. [5] PS Hagan, D Kumar, AS Lesniewski, and DE Woodward. Managing Smile Risk. Wilmott, 2002. [6] PS Hagan and AS Lesniewski. LIBOR Market Model with SABR Style Stochastic Volatility. Working Paper, 2006.

[7] PS Hagan, AS Lesniewski, and DE Woodward. Probability Distribution in the SABR Model of Stochastic Volatility. 2005. [8] I Karatzas and SE Shreve. Brownian Motion and Stochastic Calculus. Springer-Verlag, New York, 1991.

[9] F Mercurio and A Pallavicini. Swaption, Skews and Convexity Adjust- ments. Working Paper, 2005. [10] L Wu and F Zhang. LIBOR Market Model with Stochastic Volatility. Journal of Industrial and Management Optimization, 2(2):199–227, 2006.

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29. H. Neunzert 4. F.-Th. Lentes, N. Siedow 18. E. Carrizosa, H. W. Hamacher, R. Klein, »Denn nichts ist für den Menschen als Men- Three-dimensional Radiative Heat Transfer S. Nickel schen etwas wert, was er nicht mit Leiden- in Glass Cooling Processes Solving nonconvex planar location prob- schaft tun kann« (23 pages, 1998) lems by finite dominating sets Vortrag anlässlich der Verleihung des Keywords: Continuous Location, Polyhedral Gauges, Akademiepreises des Landes Rheinland- 5. A. Klar, R. Wegener Finite Dominating Sets, Approximation, Sandwich Algo- rithm, Greedy Algorithm Pfalz am 21.11.2001 A hierarchy of models for multilane vehicu- (19 pages, 2000) Keywords: Lehre, Forschung, angewandte Mathematik, lar traffic Mehrskalenanalyse, Strömungsmechanik Part I: Modeling (18 pages, 2001) (23 pages, 1998) 19. A. Becker A Review on Image Distortion Measures Part II: Numerical and stochastic investigations Keywords: Distortion measure, human visual system 30. J. Kuhnert, S. Tiwari (17 pages, 1998) (26 pages, 2000) Finite pointset method based on the projection method for simulations of the incompressible Navier-Stokes equations 6. A. Klar, N. Siedow 20. H. W. Hamacher, M. Labbé, S. Nickel, Keywords: Incompressible Navier-Stokes equations, T. Sonneborn Boundary Layers and Domain Decomposi- Meshfree method, Projection method, Particle scheme, tion for Radiative Heat Transfer and Diffu- Polyhedral Properties of the Uncapacitated Least squares approximation sion Equations: Applications to Glass Manu- Multiple Allocation Hub Location Problem AMS subject classification: 76D05, 76M28 facturing Processes Keywords: integer programming, hub location, facility (25 pages, 2001) (24 pages, 1998) location, valid inequalities, facets, branch and cut (21 pages, 2000) 31. R. Korn, M. Krekel 7. I. Choquet Optimal Portfolios with Fixed Consumption Heterogeneous catalysis modelling and 21. H. W. Hamacher, A. Schöbel or Income Streams numerical simulation in rarified gas flows Design of Zone Tariff Systems in Public Keywords: Portfolio optimisation, stochastic control, Part I: Coverage locally at equilibrium Transportation HJB equation, discretisation of control problems (30 pages, 2001) (24 pages, 1998) (23 pages, 2002)

8. J. Ohser, B. Steinbach, C. Lang 22. D. Hietel, M. Junk, R. Keck, D. Teleaga 32. M. Krekel Efficient Texture Analysis of Binary Images The Finite-Volume-Particle Method for Optimal portfolios with a loan dependent (17 pages, 1998) Conservation Laws credit spread (16 pages, 2001) Keywords: Portfolio optimisation, stochastic control, HJB equation, credit spread, log utility, power utility, 9. J. Orlik non-linear wealth dynamics 23. T. Bender, H. Hennes, J. Kalcsics, M. T. Melo, Homogenization for viscoelasticity of the (25 pages, 2002) integral type with aging and shrinkage S. Nickel (20 pages, 1998) Location Software and Interface with GIS and Supply Chain Management 33. J. Ohser, W. Nagel, K. Schladitz Keywords: facility location, software development, The Euler number of discretized sets – on the 10. J. Mohring geographical information systems, supply chain man- choice of adjacency in homogeneous lattices Helmholtz Resonators with Large Aperture agement Keywords: image analysis, Euler number, neighborhod (21 pages, 1998) (48 pages, 2001) relationships, cuboidal lattice (32 pages, 2002) 34. I. Ginzburg, K. Steiner Keywords: multiple criteria optimization, representa- 53. S. Kruse Lattice Boltzmann Model for Free-Surface tive systems of Pareto solutions, adaptive triangulation, On the Pricing of Forward Starting Options flow and Its Application to Filling Process in clustering and disaggregation techniques, visualization under Stochastic Volatility of Pareto solutions, medical physics, external beam ra- Casting Keywords: Option pricing, forward starting options, diotherapy planning, intensity modulated radiotherapy Keywords: Lattice Boltzmann models; free-surface phe- Heston model, stochastic volatility, cliquet options (31 pages, 2003) nomena; interface boundary conditions; filling pro- (11 pages, 2003) cesses; injection molding; volume of fluid method; interface boundary conditions; advection-schemes; up- 44. T. Halfmann, T. Wichmann 54. O. Iliev, D. Stoyanov wind-schemes Overview of Symbolic Methods in Industrial (54 pages, 2002) Multigrid – adaptive local refinement solver Analog Circuit Design for incompressible flows Keywords: CAD, automated analog circuit design, sym- Keywords: Navier-Stokes equations, incompressible flow, bolic analysis, computer algebra, behavioral modeling, 35. M. Günther, A. Klar, T. Materne, projection-type splitting, SIMPLE, multigrid methods, system simulation, circuit sizing, macro modeling, dif- R. Wegener adaptive local refinement, lid-driven flow in a cavity ferential-algebraic equations, index Multivalued fundamental diagrams and stop (37 pages, 2003) (17 pages, 2003) and go waves for continuum traffic equations Keywords: traffic flow, macroscopic equations, kinetic 55. V. Starikovicius 45. S. E. Mikhailov, J. Orlik derivation, multivalued fundamental diagram, stop and The multiphase flow and heat transfer in go waves, phase transitions Asymptotic Homogenisation in Strength porous media (25 pages, 2002) and Fatigue Durability Analysis of Compos- Keywords: Two-phase flow in porous media, various ites formulations, global pressure, multiphase mixture mod- 36. S. Feldmann, P. Lang, D. Prätzel-Wolters Keywords: multiscale structures, asymptotic homoge- el, numerical simulation Parameter influence on the zeros of net- nization, strength, fatigue, singularity, non-local con- (30 pages, 2003) ditions work determinants (14 pages, 2003) Keywords: Networks, Equicofactor matrix polynomials, 56. P. Lang, A. Sarishvili, A. Wirsen Realization theory, Matrix perturbation theory Blocked neural networks for knowledge ex- (30 pages, 2002) 46. P. Domínguez-Marín, P. Hansen, traction in the software development process N. Mladenovic , S. Nickel Keywords: Blocked Neural Networks, Nonlinear Regres- 37. K. Koch, J. Ohser, K. Schladitz Heuristic Procedures for Solving the sion, Knowledge Extraction, Code Inspection Spectral theory for random closed sets and Discrete Ordered Median Problem (21 pages, 2003) estimating the covariance via frequency Keywords: genetic algorithms, variable neighborhood search, discrete facility location space (31 pages, 2003) 57. H. Knaf, P. Lang, S. Zeiser Keywords: Random set, Bartlett spectrum, fast Fourier Diagnosis aiding in Regulation transform, power spectrum Thermography using Fuzzy Logic (28 pages, 2002) 47. N. Boland, P. Domínguez-Marín, S. Nickel, Keywords: fuzzy logic,knowledge representation, J. Puerto expert system 38. D. d’Humières, I. Ginzburg Exact Procedures for Solving the Discrete (22 pages, 2003) Multi-reflection boundary conditions for Ordered Median Problem Keywords: discrete location, Integer programming lattice Boltzmann models 58. M. T. Melo, S. Nickel, F. Saldanha da Gama (41 pages, 2003) Keywords: lattice Boltzmann equation, boudary condis- Largescale models for dynamic multi tions, bounce-back rule, Navier-Stokes equation commodity capacitated facility location (72 pages, 2002) 48. S. Feldmann, P. Lang Keywords: supply chain management, strategic Padé-like reduction of stable discrete linear planning, dynamic location, modeling 39. R. Korn systems preserving their stability (40 pages, 2003) Elementare Finanzmathematik Keywords: Discrete linear systems, model reduction, stability, Hankel matrix, Stein equation Keywords: Finanzmathematik, Aktien, Optionen, Port 59. J. Orlik (16 pages, 2003) folio-Optimierung, Börse, Lehrerweiterbildung, Mathe- Homogenization for contact problems with matikunterricht (98 pages, 2002) periodically rough surfaces 49. J. Kallrath, S. Nickel Keywords: asymptotic homogenization, contact problems A Polynomial Case of the Batch Presorting (28 pages, 2004) 40. J. Kallrath, M. C. Müller, S. Nickel Problem Batch Presorting Problems: Keywords: batch presorting problem, online optimization, 60. A. Scherrer, K.-H. Küfer, M. Monz, Models and Complexity Results competetive analysis, polynomial algorithms, logistics F. Alonso, T. Bortfeld Keywords: Complexity theory, Integer programming, (17 pages, 2003) Assigment, Logistics IMRT planning on adaptive volume structures – a significant advance of computa- (19 pages, 2002) 50. T. Hanne, H. L. Trinkaus tional complexity knowCube for MCDM – Keywords: Intensity-modulated radiation therapy 41. J. Linn Visual and Interactive Support for (IMRT), inverse treatment planning, adaptive volume On the frame-invariant description of the Multicriteria Decision Making structures, hierarchical clustering, local refinement, phase space of the Folgar-Tucker equation Key words: Multicriteria decision making, knowledge adaptive clustering, convex programming, mesh gener- Key words: fiber orientation, Folgar-Tucker equation, in- management, decision support systems, visual interfac- ation, multi-grid methods jection molding es, interactive navigation, real-life applications. (24 pages, 2004) (5 pages, 2003) (26 pages, 2003) 61. D. Kehrwald 42. T. Hanne, S. Nickel 51. O. Iliev, V. Laptev Parallel lattice Boltzmann simulation A Multi-Objective Evolutionary Algorithm On Numerical Simulation of Flow Through of complex flows for Scheduling and Inspection Planning in Oil Filters Keywords: Lattice Boltzmann methods, parallel com- Software Development Projects Keywords: oil filters, coupled flow in plain and porous puting, microstructure simulation, virtual material de- Key words: multiple objective programming, project media, Navier-Stokes, Brinkman, numerical simulation sign, pseudo-plastic fluids, liquid composite moulding management and scheduling, software development, (8 pages, 2003) (12 pages, 2004) evolutionary algorithms, efficient set (29 pages, 2003) 52. W. Dörfler, O. Iliev, D. Stoyanov, D. Vassileva 62. O. Iliev, J. Linn, M. Moog, D. Niedziela, On a Multigrid Adaptive Refinement Solver V. Starikovicius 43. T. Bortfeld , K.-H. Küfer, M. Monz, for Saturated Non-Newtonian Flow in On the Performance of Certain Iterative A. Scherrer, C. Thieke, H. Trinkaus Porous Media Solvers for Coupled Systems Arising in Dis- Intensity-Modulated Radiotherapy - A Large Keywords: Nonlinear multigrid, adaptive refinement, cretization of Non-Newtonian Flow Equa- Scale Multi-Criteria Programming Problem non-Newtonian flow in porous media tions (17 pages, 2003) Keywords: Performance of iterative solvers, Precondi- 72. K. Schladitz, S. Peters, D. Reinel-Bitzer, 81. N. Marheineke, R. Wegener tioners, Non-Newtonian flow A. Wiegmann, J. Ohser Fiber Dynamics in Turbulent Flows (17 pages, 2004) Design of acoustic trim based on geometric Part I: General Modeling Framework modeling and flow simulation for non-woven Keywords: fiber-fluid interaction; Cosserat rod; turbu- 63. R. Ciegis, O. Iliev, S. Rief, K. Steiner Keywords: random system of fibers, Poisson lence modeling; Kolmogorov’s energy spectrum; dou- On Modelling and Simulation of Different line process, flow resistivity, acoustic absorption, ble-velocity correlations; differentiable Gaussian fields Regimes for Liquid Polymer Moulding Lattice-Boltzmann method, non-woven (20 pages, 2005) Keywords: Liquid Polymer Moulding, Modelling, Simu- (21 pages, 2005) lation, Infiltration, Front Propagation, non-Newtonian Part II: Specific Taylor Drag flow in porous media 73. V. Rutka, A. Wiegmann Keywords: flexible fibers; k-e turbulence model; fi- (43 pages, 2004) Explicit Jump Immersed Interface Method ber-turbulence interaction scales; air drag; random for virtual material design of the effective Gaussian aerodynamic force; white noise; stochastic differential equations; ARMA process 64. T. Hanne, H. Neu elastic moduli of composite materials (18 pages, 2005) Simulating Human Resources in Keywords: virtual material design, explicit jump im- Software Development Processes mersed interface method, effective elastic moduli, Keywords: Human resource modeling, software process, composite materials 82. C. H. Lampert, O. Wirjadi productivity, human factors, learning curve (22 pages, 2005) An Optimal Non-Orthogonal Separation of (14 pages, 2004) the Anisotropic Gaussian Convolution Filter 74. T. Hanne Keywords: Anisotropic Gaussian filter, linear filtering, orientation space, nD image processing, separable filters 65. O. Iliev, A. Mikelic, P. Popov Eine Übersicht zum Scheduling von Baustellen (25 pages, 2005) Fluid structure interaction problems in de- Keywords: Projektplanung, Scheduling, Bauplanung, formable porous media: Toward permeabil- Bauindustrie ity of deformable porous media (32 pages, 2005) 83. H. Andrä, D. Stoyanov Keywords: fluid-structure interaction, deformable po- Error indicators in the parallel finite ele- rous media, upscaling, linear elasticity, stokes, finite el- 75. J. Linn ment solver for linear elasticity DDFEM ements The Folgar-Tucker Model as a Differetial Keywords: linear elasticity, finite element method, hier- (28 pages, 2004) Algebraic System for Fiber Orientation archical shape functions, domain decom-position, parallel implementation, a posteriori error estimates Calculation (21 pages, 2006) 66. F. Gaspar, O. Iliev, F. Lisbona, A. Naumovich, Keywords: fiber orientation, Folgar–Tucker model, in- P. Vabishchevich variants, algebraic constraints, phase space, trace sta- On numerical solution of 1-D poroelasticity bility 84. M. Schröder, I. Solchenbach equations in a multilayered domain (15 pages, 2005) Optimization of Transfer Quality in Keywords: poroelasticity, multilayered material, finite Regional Public Transit volume discretization, MAC type grid 76. M. Speckert, K. Dreßler, H. Mauch, Keywords: public transit, transfer quality, quadratic (41 pages, 2004) A. Lion, G. J. Wierda assignment problem (16 pages, 2006) Simulation eines neuartigen Prüfsystems 67. J. Ohser, K. Schladitz, K. Koch, M. Nöthe für Achserprobungen durch MKS-Model- Diffraction by image processing and its ap- lierung einschließlich Regelung 85. A. Naumovich, F. J. Gaspar plication in materials science Keywords: virtual test rig, suspension testing, On a multigrid solver for the three-dimen- Keywords: porous microstructure, image analysis, ran- multibody simulation, modeling hexapod test rig, opti- sional Biot poroelasticity system in multi- dom set, fast Fourier transform, power spectrum, Bar- mization of test rig configuration layered domains tlett spectrum (20 pages, 2005) Keywords: poroelasticity, interface problem, multigrid, (13 pages, 2004) operator-dependent prolongation 77. K.-H. Küfer, M. Monz, A. Scherrer, P. Süss, (11 pages, 2006) 68. H. Neunzert F. Alonso, A. S. A. Sultan, Th. Bortfeld, Mathematics as a Technology: Challenges D. Craft, Chr. Thieke 86. S. Panda, R. Wegener, N. Marheineke for the next 10 Years Multicriteria optimization in intensity Slender Body Theory for the Dynamics of Keywords: applied mathematics, technology, modelling, modulated radiotherapy planning Curved Viscous Fibers simulation, visualization, optimization, glass processing, Keywords: multicriteria optimization, extreme solu- Keywords: curved viscous fibers; fluid dynamics; Navier- spinning processes, fiber-fluid interaction, trubulence tions, real-time decision making, adaptive approxima- Stokes equations; free boundary value problem; asymp- effects, topological optimization, multicriteria optimization schemes, clustering methods, IMRT planning, re- totic expansions; slender body theory tion, Uncertainty and Risk, financial mathematics, Mal- verse engineering (14 pages, 2006) liavin calculus, Monte-Carlo methods, virtual material (51 pages, 2005) design, filtration, bio-informatics, system biology 87. E. Ivanov, H. Andrä, A. Kudryavtsev (29 pages, 2004) 78. S. Amstutz, H. Andrä Domain Decomposition Approach for Auto- A new algorithm for topology optimization matic Parallel Generation of Tetrahedral Grids 69. R. Ewing, O. Iliev, R. Lazarov, A. Naumovich using a level-set method Key words: Grid Generation, Unstructured Grid, Delau- On convergence of certain finite difference Keywords: shape optimization, topology optimization, nay Triangulation, Parallel Programming, Domain De- discretizations for 1D poroelasticity inter- topological sensitivity, level-set composition, Load Balancing face problems (22 pages, 2005) (18 pages, 2006) Keywords: poroelasticity, multilayered material, finite volume discretizations, MAC type grid, error estimates 79. N. Ettrich 88. S. Tiwari, S. Antonov, D. Hietel, J. Kuhnert, (26 pages,2004) Generation of surface elevation models for R. Wegener urban drainage simulation A Meshfree Method for Simulations of In- 70. W. Dörfler, O. Iliev, D. Stoyanov, D. Vassileva Keywords: Flooding, simulation, urban elevation teractions between Fluids and Flexible On Efficient Simulation of Non-Newto- models, laser scanning Structures nian Flow in Saturated Porous Media with a (22 pages, 2005) Key words: Meshfree Method, FPM, Fluid Structure Multigrid Adaptive Refinement Solver Interaction, Sheet of Paper, Dynamical Coupling Keywords: Nonlinear multigrid, adaptive renement, 80. H. Andrä, J. Linn, I. Matei, I. Shklyar, (16 pages, 2006) non-Newtonian in porous media K. Steiner, E. Teichmann (25 pages, 2004) OPTCAST – Entwicklung adäquater Struk- 89. R. Ciegis , O. Iliev, V. Starikovicius, K. Steiner turoptimierungsverfahren für Gießereien Numerical Algorithms for Solving Problems 71. J. Kalcsics, S. Nickel, M. Schröder Technischer Bericht (KURZFASSUNG) of Multiphase Flows in Porous Media Towards a Unified Territory Design Approach Keywords: Topologieoptimierung, Level-Set-Methode, Keywords: nonlinear algorithms, finite-volume method, – Applications, Algorithms and GIS Integration Gießprozesssimulation, Gießtechnische Restriktionen, software tools, porous media, flows Keywords: territory desgin, political districting, sales CAE-Kette zur Strukturoptimierung (16 pages, 2006) territory alignment, optimization algorithms, Geo- (77 pages, 2005) graphical Information Systems (40 pages, 2005) 90. D. Niedziela, O. Iliev, A. Latz Keywords: Elastic BVP, elastoplastic BVP, variational 109. Ph. Süss, K.-H. Küfer On 3D Numerical Simulations of Viscoelastic inequalities, rate-independency, hysteresis, linear kine- Smooth intensity maps and the Bortfeld- Fluids matic hardening, stop- and play-operator Boyer sequencer (21 pages, 2006) Keywords: non-Newtonian fluids, anisotropic viscosity, Keywords: probabilistic analysis, intensity modulated integral constitutive equation radiotherapy treatment (IMRT), IMRT plan application, (18 pages, 2006) 100. M. Speckert, K. Dreßler, H. Mauch step-and-shoot sequencing MBS Simulation of a hexapod based sus- (8 pages, 2007) 91. A. Winterfeld pension test rig Application of general semi-infinite Pro- Keywords: Test rig, MBS simulation, suspension, 110. E. Ivanov, O. Gluchshenko, H. Andrä, gramming to Lapidary Cutting Problems hydraulics, controlling, design optimization A. Kudryavtsev (12 pages, 2006) Keywords: large scale optimization, nonlinear program- Parallel software tool for decomposing and ming, general semi-infinite optimization, design center- meshing of 3d structures ing, clustering 101. S. Azizi Sultan, K.-H. Küfer Keywords: a-priori domain decomposition, unstruc- (26 pages, 2006) A dynamic algorithm for beam orientations tured grid, Delaunay mesh generation in multicriteria IMRT planning (14 pages, 2007) 92. J. Orlik, A. Ostrovska Keywords: radiotherapy planning, beam orientation Space-Time Finite Element Approximation optimization, dynamic approach, evolutionary algo- 111. O. Iliev, R. Lazarov, J. Willems and Numerical Solution of Hereditary rithm, global optimization Numerical study of two-grid precondition- (14 pages, 2006) Linear Viscoelasticity Problems ers for 1d elliptic problems with highly Keywords: hereditary viscoelasticity; kern approxima- oscillating discontinuous coefficients tion by interpolation; space-time finite element approxi- 102. T. Götz, A. Klar, N. Marheineke, R. Wegener Keywords: two-grid algorithm, oscillating coefficients, mation, stability and a priori estimate A Stochastic Model for the Fiber Lay-down preconditioner (24 pages, 2006) Process in the Nonwoven Production (20 pages, 2007) Keywords: fiber dynamics, stochastic Hamiltonian sys- 93. V. Rutka, A. Wiegmann, H. Andrä tem, stochastic averaging 112. L. Bonilla, T. Götz, A. Klar, N. Marheineke, (17 pages, 2006) EJIIM for Calculation of effective Elastic R. Wegener Moduli in 3D Linear Elasticity Hydrodynamic limit of the Fokker-Planck- Keywords: Elliptic PDE, linear elasticity, irregular do- 103. Ph. Süss, K.-H. Küfer equation describing fiber lay-down pro- main, finite differences, fast solvers, effective elas- Balancing control and simplicity: a variable cesses tic moduli aggregation method in intensity modulated Keywords: stochastic dierential equations, Fokker- (24 pages, 2006) radiation therapy planning Planck equation, asymptotic expansion, Ornstein- Keywords: IMRT planning, variable aggregation, clus- Uhlenbeck process 94. A. Wiegmann, A. Zemitis tering methods (17 pages, 2007) EJ-HEAT: A Fast Explicit Jump Harmonic (22 pages, 2006) Averaging Solver for the Effective Heat 113. S. Rief Conductivity of Composite Materials 104. A. Beaudry, G. Laporte, T. Melo, S. Nickel Modeling and simulation of the pressing Keywords: Stationary heat equation, effective ther- Dynamic transportation of patients in hos- section of a paper machine mal conductivity, explicit jump, discontinuous coeffi- pitals Keywords: paper machine, computational fluid dynam- cients, virtual material design, microstructure simula- Keywords: in-house hospital transportation, dial-a-ride, ics, porous media tion, EJ-HEAT dynamic mode, tabu search (41 pages, 2007) (21 pages, 2006) (37 pages, 2006) 114. R. Ciegis, O. Iliev, Z. Lakdawala 95. A. Naumovich 105. Th. Hanne On parallel numerical algorithms for simu- On a finite volume discretization of the Applying multiobjective evolutionary algo- lating industrial filtration problems three-dimensional Biot poroelasticity sys- rithms in industrial projects Keywords: Navier-Stokes-Brinkmann equations, finite tem in multilayered domains Keywords: multiobjective evolutionary algorithms, dis- volume discretization method, SIMPLE, parallel comput- Keywords: Biot poroelasticity system, interface problems, crete optimization, continuous optimization, electronic ing, data decomposition method finite volume discretization, finite difference method circuit design, semi-infinite programming, scheduling (24 pages, 2007) (21 pages, 2006) (18 pages, 2006) 115. N. Marheineke, R. Wegener 96. M. Krekel, J. Wenzel 106. J. Franke, S. Halim Dynamics of curved viscous fibers with sur- A unified approach to Credit Default Swap Wild bootstrap tests for comparing signals face tension tion and Constant Maturity Credit Default and images Keywords: Slender body theory, curved viscous bers Swap valuation Keywords: wild bootstrap test, texture classification, with surface tension, free boundary value problem Keywords: LIBOR market model, credit risk, Credit De- textile quality control, defect detection, kernel estimate, (25 pages, 2007) fault Swaption, Constant Maturity Credit Default Swap- nonparametric regression method (13 pages, 2007) 116. S. Feth, J. Franke, M. Speckert (43 pages, 2006) Resampling-Methoden zur mse-Korrektur 107. Z. Drezner, S. Nickel und Anwendungen in der Betriebsfestigkeit 97. A. Dreyer Solving the ordered one-median problem in Keywords: Weibull, Bootstrap, Maximum-Likelihood, Interval Methods for Analog Circiuts the plane Betriebsfestigkeit Keywords: interval arithmetic, analog circuits, tolerance Keywords: planar location, global optimization, ordered (16 pages, 2007) analysis, parametric linear systems, frequency response, median, big triangle small triangle method, bounds, symbolic analysis, CAD, computer algebra numerical experiments 117. H. Knaf (36 pages, 2006) (21 pages, 2007) Kernel Fisher discriminant functions – a con- cise and rigorous introduction 98. N. Weigel, S. Weihe, G. Bitsch, K. Dreßler 108. Th. Götz, A. Klar, A. Unterreiter, Keywords: wild bootstrap test, texture classification, Usage of Simulation for Design and Optimi- R. Wegener textile quality control, defect detection, kernel estimate, zation of Testing Numerical evidance for the non-existing of nonparametric regression Keywords: Vehicle test rigs, MBS, control, hydraulics, solutions of the equations desribing rota- (30 pages, 2007) testing philosophy tional fiber spinning (14 pages, 2006) Keywords: rotational fiber spinning, viscous fibers, 118. O. Iliev, I. Rybak boundary value problem, existence of solutions On numerical upscaling for flows in hetero- 99. H. Lang, G. Bitsch, K. Dreßler, M. Speckert (11 pages, 2007) geneous porous media Comparison of the solutions of the elastic and elastoplastic boundary value problems Keywords: numerical upscaling, heterogeneous porous 128. M. Krause, A. Scherrer 137. E. Savenkov, H. Andrä, O. Iliev∗ media, single phase flow, Darcy‘s law, multiscale prob- On the role of modeling parameters in IMRT An analysis of one regularization approach lem, effective permeability, multipoint flux approxima- plan optimization for solution of pure Neumann problem tion, anisotropy Keywords: intensity-modulated radiotherapy (IMRT), Keywords: pure Neumann problem, elasticity, regular- (17 pages, 2007) inverse IMRT planning, convex optimization, sensitiv- ization, finite element method, condition number ity analysis, elasticity, modeling parameters, equivalent (27 pages, 2008) 119. O. Iliev, I. Rybak uniform dose (EUD) (18 pages, 2007) On approximation property of multipoint 138. O. Berman, J. Kalcsics, D. Krass, S. Nickel flux approximation method The ordered gradual covering location Keywords: Multipoint flux approximation, finite volume 129. A. Wiegmann problem on a network method, elliptic equation, discontinuous tensor coeffi- Computation of the permeability of porous Keywords: gradual covering, ordered median function, cients, anisotropy materials from their microstructure by FFF- network location (15 pages, 2007) Stokes (32 pages, 2008) Keywords: permeability, numerical homogenization, 120. O. Iliev, I. Rybak, J. Willems fast Stokes solver 139. S. Gelareh, S. Nickel (24 pages, 2007) On upscaling heat conductivity for a class of Multi-period public transport design: A industrial problems novel model and solution approaches Keywords: Multiscale problems, effective heat conduc- 130. T. Melo, S. Nickel, F. Saldanha da Gama Keywords: Integer programming, hub location, public tivity, numerical upscaling, domain decomposition Facility Location and Supply Chain Manage- transport, multi-period planning, heuristics (21 pages, 2007) ment – A comprehensive review (31 pages, 2008) Keywords: facility location, supply chain management, 121. R. Ewing, O. Iliev, R. Lazarov, I. Rybak network design 140. T. Melo, S. Nickel, F. Saldanha-da-Gama (54 pages, 2007) On two-level preconditioners for flow in Network design decisions in supply chain porous media planning Keywords: Multiscale problem, Darcy‘s law, single 131. T. Hanne, T. Melo, S. Nickel Keywords: supply chain design, integer programming phase flow, anisotropic heterogeneous porous media, Bringing robustness to patient flow models, location models, heuristics numerical upscaling, multigrid, domain decomposition, management through optimized patient (20 pages, 2008) efficient preconditioner (18 pages, 2007) transports in hospitals Keywords: Dial-a-Ride problem, online problem, case 141. C. Lautensack, A. Särkkä, J. Freitag, study, tabu search, hospital logistics K. Schladitz 122. M. Brickenstein, A. Dreyer (23 pages, 2007) POLYBORI: A Gröbner basis framework Anisotropy analysis of pressed point processes for Boolean polynomials 132. R. Ewing, O. Iliev, R. Lazarov, I. Rybak, Keywords: Gröbner basis, formal verification, Boolean Keywords: estimation of compression, isotropy test, J. Willems polynomials, algebraic cryptoanalysis, satisfiability nearest neighbour distance, orientation analysis, polar (23 pages, 2007) An efficient approach for upscaling proper- ice, Ripley’s K function ties of composite materials with high con- (35 pages, 2008) trast of coefficients 123. O. Wirjadi Keywords: effective heat conductivity, permeability of 142. O. Iliev, R. Lazarov, J. Willems Survey of 3d image segmentation methods fractured porous media, numerical upscaling, fibrous A Graph-Laplacian approach for calculating Keywords: image processing, 3d, image segmentation, insulation materials, metal foams the effective thermal conductivity of com- binarization (16 pages, 2008) (20 pages, 2007) plicated fiber geometries Keywords: graph laplacian, effective heat conductivity, 133. S. Gelareh, S. Nickel numerical upscaling, fibrous materials 124. S. Zeytun, A. Gupta New approaches to hub location problems (14 pages, 2008) A Comparative Study of the Vasicek and the in public transport planning CIR Model of the Short Rate Keywords: integer programming, hub location, trans- 143. J. Linn, T. Stephan, J. Carlsson, R. Bohlin Keywords: interest rates, Vasicek model, CIR-model, portation, decomposition, heuristic Fast simulation of quasistatic rod deforma- calibration, parameter estimation (25 pages, 2008) (17 pages, 2007) tions for VR applications Keywords: quasistatic deformations, geometrically 134. G. Thömmes, J. Becker, M. Junk, A. K. Vai- exact rod models, variational formulation, energy min- 125. G. Hanselmann, A. Sarishvili kuntam, D. Kehrwald, A. Klar, K. Steiner, imization, finite differences, nonlinear conjugate gra- Heterogeneous redundancy in software A. Wiegmann dients quality prediction using a hybrid Bayesian A Lattice Boltzmann Method for immiscible (7 pages, 2008) approach multiphase flow simulations using theLevel Keywords: reliability prediction, fault prediction, non- Set Method 144. J. Linn, T. Stephan homogeneous poisson process, Bayesian model aver- Keywords: Lattice Boltzmann method, Level Set aging Simulation of quasistatic deformations us- method, free surface, multiphase flow (17 pages, 2007) ing discrete rod models (28 pages, 2008) Keywords: quasistatic deformations, geometrically exact rod models, variational formulation, energy min- 126. V. Maag, M. Berger, A. Winterfeld, K.-H. 135. J. Orlik imization, finite differences, nonlinear conjugate gra- Küfer Homogenization in elasto-plasticity dients (9 pages, 2008) A novel non-linear approach to minimal Keywords: multiscale structures, asymptotic homogeni- area rectangular packing zation, nonlinear energy Keywords: rectangular packing, non-overlapping con- (40 pages, 2008) 145. J. Marburger, N. Marheineke, R. Pinnau straints, non-linear optimization, regularization, relax- Adjoint based optimal control using mesh- ation (18 pages, 2007) 136. J. Almquist, H. Schmidt, P. Lang, J. Deitmer, less discretizations M. Jirstrand, D. Prätzel-Wolters, H. Becker Keywords: Mesh-less methods, particle methods, Eul- Determination of interaction between erian-Lagrangian formulation, optimization strategies, 127. M. Monz, K.-H. Küfer, T. Bortfeld, C. Thieke adjoint method, hyperbolic equations MCT1 and CAII via a mathematical and Pareto navigation – systematic multi-crite- (14 pages, 2008 physiological approach ria-based IMRT treatment plan determina- Keywords: mathematical modeling; model reduction; tion electrophysiology; pH-sensitive microelectrodes; pro- 146. S. Desmettre, J. Gould, A. Szimayer Keywords: convex, interactive multi-objective optimiza- ton antenna Own-company stockholding and work effort tion, intensity modulated radiotherapy planning (20 pages, 2008) preferences of an unconstrained executive (15 pages, 2007) Keywords: optimal portfolio choice, executive compen- sation (33 pages, 2008) 147. M. Berger, M. Schröder, K.-H. Küfer Keywords: Fiber-fluid interaction, slender-body theory, 166. J. I. Serna, M. Monz, K.-H. Küfer, C. Thieke A constraint programming approach for the turbulence modeling, model reduction, stochastic dif- Trade-off bounds and their effect in multi- two-dimensional rectangular packing prob- ferential equations, Fokker-Planck equation, asymptotic criteria IMRT planning expansions, parameter identification lem with orthogonal orientations Keywords: trade-off bounds, multi-criteria optimization, (21 pages, 2009) Keywords: rectangular packing, orthogonal orienta- IMRT, Pareto surface tions non-overlapping constraints, constraint propa- (15 pages, 2009) gation 157. E. Glatt, S. Rief, A. Wiegmann, M. Knefel, (13 pages, 2008) E. Wegenke 167. W. Arne, N. Marheineke, A. Meister, R. We- Structure and pressure drop of real and vir- gener 148. K. Schladitz, C. Redenbach, T. Sych, tual metal wire meshes Numerical analysis of Cosserat rod and M. Godehardt Keywords: metal wire mesh, structure simulation, string models for viscous jets in rotational model calibration, CFD simulation, pressure loss Microstructural characterisation of open spinning processes (7 pages, 2009) foams using 3d images Keywords: Rotational spinning process, curved viscous Keywords: virtual material design, image analysis, open fibers, asymptotic Cosserat models, boundary value foams 158. S. Kruse, M. Müller problem, existence of numerical solutions (30 pages, 2008) Pricing American call options under the as- (18 pages, 2009) sumption of stochastic dividends – An ap- 149. E. Fernández, J. Kalcsics, S. Nickel, plication of the Korn-Rogers model 168. T. Melo, S. Nickel, F. Saldanha-da-Gama R. Ríos-Mercado Keywords: option pricing, American options, dividends, An LP-rounding heuristic to solve a multi- A novel territory design model arising in dividend discount model, Black-Scholes model period facility relocation problem (22 pages, 2009) the implementation of the WEEE-Directive Keywords: supply chain design, heuristic, linear pro- Keywords: heuristics, optimization, logistics, recycling gramming, rounding (28 pages, 2008) 159. H. Lang, J. Linn, M. Arnold (37 pages, 2009) Multibody dynamics simulation of geomet- 150. H. Lang, J. Linn rically exact Cosserat rods 169. I. Correia, S. Nickel, F. Saldanha-da-Gama Lagrangian field theory in space-time for Keywords: flexible multibody dynamics, large deforma- Single-allocation hub location problems tions, finite rotations, constrained mechanical systems, geometrically exact Cosserat rods with capacity choices structural dynamics Keywords: Cosserat rods, geometrically exact rods, Keywords: hub location, capacity decisions, MILP for- (20 pages, 2009) small strain, large deformation, deformable bodies, mulations Lagrangian field theory, variational calculus (27 pages, 2009) (19 pages, 2009) 160. P. Jung, S. Leyendecker, J. Linn, M. Ortiz Discrete Lagrangian mechanics and geo- 170. S. Acar, K. Natcheva-Acar 151. K. Dreßler, M. Speckert, R. Müller, metrically exact Cosserat rods A guide on the implementation of the Ch. Weber Keywords: special Cosserat rods, Lagrangian mechanics, Heath-Jarrow-Morton Two-Factor Gaussian Noether’s theorem, discrete mechanics, frame-indiffer- Customer loads correlation in truck engi- Short Rate Model (HJM-G2++) ence, holonomic constraints Keywords: short rate model, two factor Gaussian, neering (14 pages, 2009) Keywords: Customer distribution, safety critical compo- G2++, option pricing, calibration nents, quantile estimation, Monte-Carlo methods (30 pages, 2009) (11 pages, 2009) 161. M. Burger, K. Dreßler, A. Marquardt, M. Speckert 171. A. Szimayer, G. Dimitroff, S. Lorenz 152. H. Lang, K. Dreßler Calculating invariant loads for system simu- A parsimonious multi-asset Heston model: An improved multiaxial stress-strain correc- lation in vehicle engineering calibration and derivative pricing Keywords: iterative learning control, optimal control tion model for elastic FE postprocessing Keywords: Heston model, multi-asset, option pricing, theory, differential algebraic equations (DAEs) Keywords: Jiang’s model of elastoplasticity, stress-strain calibration, correlation (18 pages, 2009) correction, parameter identification, automatic differ- (28 pages, 2009) entiation, least-squares optimization, Coleman-Li algorithm 162. M. Speckert, N. Ruf, K. Dreßler 172. N. Marheineke, R. Wegener (6 pages, 2009) Undesired drift of multibody models excit- Modeling and validation of a stochastic ed by measured accelerations or forces drag for fibers in turbulent flows Keywords: multibody simulation, full vehicle model, 153. J. Kalcsics, S. Nickel, M. Schröder Keywords: fiber-fluid interactions, long slender fibers, force-based simulation, drift due to noise A generic geometric approach to territory turbulence modelling, aerodynamic drag, dimensional (19 pages, 2009) design and districting analysis, data interpolation, stochastic partial differen- Keywords: Territory design, districting, combinatorial tial algebraic equation, numerical simulations, experi- optimization, heuristics, computational geometry 163. A. Streit, K. Dreßler, M. Speckert, J. Lichter, mental validations (32 pages, 2009) T. Zenner, P. Bach (19 pages, 2009) Anwendung statistischer Methoden zur 154. Th. Fütterer, A. Klar, R. Wegener Erstellung von Nutzungsprofilen für die 173. S. Nickel, M. Schröder, J. Steeg An energy conserving numerical scheme for Auslegung von Mobilbaggern Planning for home health care services the dynamics of hyperelastic rods Keywords: Nutzungsvielfalt, Kundenbeanspruchung, Keywords: home health care, route planning, meta- Keywords: Cosserat rod, hyperealstic, energy conserva- Bemessungsgrundlagen heuristics, constraint programming tion, finite differences (13 pages, 2009) (23 pages, 2009) (16 pages, 2009) 164. I. Correia, S. Nickel, F. Saldanha-da-Gama 174. G. Dimitroff, A. Szimayer, A. Wagner 155. A. Wiegmann, L. Cheng, E. Glatt, O. Iliev, The capacitated single-allocation hub loca- Quanto option pricing in the parsimonious S. Rief tion problem revisited: A note on a classical Heston model Design of pleated filters by computer sim- formulation Keywords: Heston model, multi asset, quanto options, ulations Keywords: Capacitated Hub Location, MIP formulations option pricing (14 pages, 2009) 174. G. Dimitroff, A. Szimayer, A. Keywords: Solid-gas separation, solid-liquid separation, (10 pages, 2009) Wagner pleated filter, design, simulation (21 pages, 2009) 165. F. Yaneva, T. Grebe, A. Scherrer An alternative view on global radiotherapy 175. S. Herkt, K. Dreßler, R. Pinnau 156. A. Klar, N. Marheineke, R. Wegener optimization problems Model reduction of nonlinear problems in Hierarchy of mathematical models for pro- Keywords: radiotherapy planning, path-connected sub- structural mechanics duction processes of technical textiles levelsets, modified gradient projection method, improv- Keywords: flexible bodies, FEM, nonlinear model reduc- ing and feasible directions tion, POD (14 pages, 2009) (13 pages, 2009) 176. M. K. Ahmad, S. Didas, J. Iqbal 185. P. Ruckdeschel 195. A. Latz, J. Zausch Using the Sharp Operator for edge detec- Optimally Robust Kalman Filtering Thermodynamic consistent transport theory tion and nonlinear diffusion Keywords: robustness, Kalman Filter, innovation outlier, of Li-Ion batteries Keywords: maximal function, sharp function,image pro- additive outlier Keywords: Li-Ion batteries, nonequilibrium thermody- cessing, edge detection, nonlinear diffusion (42 pages, 2010) namics, thermal transport, modeling (17 pages, 2009) (18 pages, 2010) 186. S. Repke, N. Marheineke, R. Pinnau 196. S. Desmettre 177. M. Speckert, N. Ruf, K. Dreßler, R. Müller, On adjoint-based optimization of a free C. Weber, S. Weihe surface Stokes flow Optimal investment for executive Ein neuer Ansatz zur Ermittlung von Er- Keywords: film casting process, thin films, free surface stockholders with exponential utility Keywords: portfolio choice, executive stockholder, probungslasten für sicherheitsrelevante Stokes flow, optimal control, Lagrange formalism (13 pages, 2010) work effort, exponential utility Bauteile (24 pages, 2010) Keywords: sicherheitsrelevante Bauteile, Kundenbean spruchung, Festigkeitsverteilung, Ausfallwahrschein- 187. O. Iliev, R. Lazarov, J. Willems 197. W. Arne, N. Marheineke, J. Schnebele, lichkeit, Konfidenz, statistische Unsicherheit, Sicher- Variational multiscale Finite Element R. Wegener heitsfaktoren Method for flows in highly porous media (16 pages, 2009) Fluid-fiber-interactions in rotational spin- Keywords: numerical upscaling, flow in heterogeneous ning process of glass wool production porous media, Brinkman equations, Darcy’s law, subgrid Keywords: Rotational spinning process, viscous thermal approximation, discontinuous Galerkin mixed FEM 178. J. Jegorovs jets, fluid-fiber-interactions, two-way coupling, slender- (21 pages, 2010) Wave based method: new applicability areas body theory, Cosserat rods, drag models, boundary Keywords: Elliptic boundary value problems, inho- value problem, continuation method mogeneous Helmholtz type differential equations in 188. S. Desmettre, A. Szimayer (20 pages, 2010) bounded domains, numerical methods, wave based Work effort, consumption, and portfolio method, uniform B-splines 198. A. Klar, J. Maringer, R. Wegener (10 pages, 2009) selection: When the occupational choice matters A 3d model for fiber lay-down in nonwoven Keywords: portfolio choice, work effort, consumption, production processes 179. H. Lang, M. Arnold occupational choice Keywords: fiber dynamics, Fokker-Planck equations, Numerical aspects in the dynamic simula- (34 pages, 2010) diffusion limits tion of geometrically exact rods (15 pages, 2010) Keywords: Kirchhoff and Cosserat rods, geometri 189. O. Iliev, Z. Lakdawala, V. Starikovicius cally exact rods, deformable bodies, multibody 199. Ch. Erlwein, M. Müller dynamics,artial differential algebraic equations, On a numerical subgrid upscaling algorithm A regime-switching regression model for method of lines, time integration for Stokes-Brinkman equations hedge funds Keywords: Stokes-Brinkman equations, subgrid (21 pages, 2009) Keywords: switching regression model, Hedge funds, approach, multiscale problems, numerical upscaling optimal parameter estimation, filtering (27 pages, 2010) 180. H. Lang (26 pages, 2011) Comparison of quaternionic and rotation- free null space formalisms for multibody 190. A. Latz, J. Zausch, O. Iliev 200. M. Dalheimer dynamics Modeling of species and charge transport in Power to the people – Das Stromnetz der Keywords: Parametrisation of rotations, differential- Li-Ion Batteries based on non-equilibrium Zukunft algebraic equations, multibody dynamics, constrained thermodynamics Keywords: Smart Grid, Stromnetz, Erneuerbare Ener- mechanical systems, Lagrangian mechanics Keywords: lithium-ion battery, battery modeling, elec- gien, Demand-Side Management (40 pages, 2010) trochemical simulation, concentrated electrolyte, ion (27 pages, 2011) transport (8 pages, 2010) 201. D. Stahl, J. Hauth 181. S. Nickel, F. Saldanha-da-Gama, H.-P. Ziegler PF-MPC: Particle Filter-Model Predictive Stochastic programming approaches for risk Control aware supply chain network design problems 191. P. Popov, Y. Vutov, S. Margenov, O. Iliev Finite volume discretization of equations Keywords: Model Predictive Control, Particle Fil- Keywords: Supply Chain Management, multi-stage sto- ter, CSTR, Inverted Pendulum, Nonlinear Systems, chastic programming, financial decisions, risk describing nonlinear diffusion in Li-Ion bat- Sequential Monte Carlo (37 pages, 2010) teries (40 pages, 2011) Keywords: nonlinear diffusion, finite volume discretiza- 182. P. Ruckdeschel, N. Horbenko tion, Newton method, Li-Ion batteries 202. G. Dimitroff, J. de Kock (9 pages, 2010) Robustness properties of estimators in gen- Calibrating and completing the volatility eralized Pareto Models cube in the SABR Model Keywords: global robustness, local robustness, finite 192. W. Arne, N. Marheineke, R. Wegener Keywords: stochastic volatility, SABR, volatility cube, sample breakdown point, generalized Pareto distribution Asymptotic transition from Cosserat rod swaption (58 pages, 2010) to string models for curved viscous iner- (12 pages, 2011) tial jets 183. P. Jung, S. Leyendecker, J. Linn, M. Ortiz Keywords: rotational spinning processes; inertial and viscous-inertial fiber regimes; asymptotic limits; slender- A discrete mechanics approach to Cosserat body theory; boundary value problems rod theory – Part 1: static equilibria (23 pages, 2010) Keywords: Special Cosserat rods; Lagrangian mechanics; Noether’s theorem; discrete mechanics; frame- indifference; holonomic constraints; variational formu- 193. L. Engelhardt, M. Burger, G. Bitsch lation Real-time simulation of multibody-systems (35 pages, 2010) for on-board applications Keywords: multibody system simulation, real-time simu- 184. R. Eymard, G. Printsypar lation, on-board simulation, Rosenbrock methods Status quo: February 2011 (10 pages, 2010) A proof of convergence of a finite volume scheme for modified steady Richards’ equation describing transport processes in the 194. M. Burger, M. Speckert, K. Dreßler pressing section of a paper machine Optimal control methods for the calculation Keywords: flow in porous media, steady Richards’ of invariant excitation signals for multibody equation, finite volume methods, convergence of systems approximate solution Keywords: optimal control, optimization, mbs simula- (14 pages, 2010) tion, invariant excitation (9 pages, 2010)