TRENDS IN MATHEMATICS
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Michael Kohlmann Shanjian Tang Editors
Springer Basel AG Editors' addresses:
Michael Kohlmann Shanjian Tang Fakultät für Mathematik und Informatik Fudan University Universität Konstanz Department of Mathematics Postfach 5560 Shanghai 200433 D-78434 Konstanz China
[email protected] currently research fellow at the University of Konstanz e-mail: [email protected]
2000 Mathematical Subject Classification 91B28; 91B02
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data
Mathematical finance / Workshop of the Mathematical Finance Research Project, Konstanz, Germany, October 5-7, 2000. Michael Kohlmann ; Shanjian Tang ed. - Basel; Boston ; Berlin : Birkhäuser, 2001 (Trends in mathematics) ISBN 978-3-0348-9506-4 ISBN 978-3-0348-8291-0 (ebook) DOI 10.1007/978-3-0348-8291-0
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© 2001 Springer Basel AG Originally published by Birkhäuser Verlag, Basel, Switzerland in 2001 Softcover reprint of the hardcover 1st edition 2001 Printed on acid-free paper produced from chlorine-free pulp. TCF °°
ISBN 978-3-0348-9506-4
98765432 1 www.birkhasuer-science.com Preface
In the centenary year of the publication of Bachelier's thesis, what today is considered as the foundation of modern finance, we had the opportunity to invite experts in this relatively new field in mathematics to participate in a meeting at the University of Konstanz, Germany. This could be the place to consider the historical development, but as Professor Girlich presented a remarkable lecture on the past of what now is known as mathematical finance, we refer the reader to the article in this volume. Instead w etak e the opportunity to express our thanks to those colleagues who made this workshop possible: to Professor Sondermann, University of Bonn, Ger• many, who in a sense initiated the idea, to our friends Mark Davis, Robert Elliott, and Xun Yu Zhou, whose advices were extremely helpful in establishing the pro• gram of the conference, and to the invited lecturers Nicole EI Karoui, Ec khard Platen, and Stan Pliska for carefully preparing their lectures. Also w egratefully appreciate our students' help during the conference and Mrs Weisser's successful efforts in providing our guests with visa and hotel reservations. Last we should mention the students of the business department who organized a great conference dinner on Mainau island and who documented the meeting in a lot of photos. Finally we thank our wives Evi and Jie for giving us leave from home (-v.ork) to organize the conference.
Konstanz, in October 2000, Michael Kohlmann and Shanjian Tang Table of Contents
Note: in the titles of co-authored papers the lecturer's name is in bold face)
Preface ...... 5
Table of Contents ...... 7
Participants ...... 11
On-line portfolio strategy with prediction Sergio Albeverio, LanJun Lao and XueLei Zhao ...... 19
Continuous time financial market, transaction cost and transaction intensity Sergio Albeverio, LanJun Lao and XueLei Zhao ...... 29
Demand Heterogeneity and Price Volatility D.R. Alexander and E.E. Haven ...... 40
Optimal default boundary in a discrete time setting Agata Altieri and Tiziano Vargiolu ...... 49
An Infinite Factor Model for the Interest Rate Derivatives Arunabha Bagchi and K. Suresh Kumar ...... 59
Arbitrage and Pricing with Collateral Jose Fajardo Barbachan ...... 69
On the existence of optimal controls for a singular stochastic control problem in finance Fred E. Benth, Kenneth H. Karlsen, and Kristin Reikvam ...... 79
A Quadratic Approach To Interest Rates Models In Incomplete Markets Francesca Biagini ...... 89
Risk Sensitive Asset Management: Two Empirical Examples T.Bielecki, A.Harris, J.Li, and S.Pliska ...... 99 8 Table of Contents
Bounded Variation Singular Stochastic Control and Associated Dynkin Game Frederik Boetius ...... 111
Option Pricing and Hedging Under Regular Levy Processes of Exponential Type Svetlana 1. Boyarchenko and Sergei Z. Levendorskll ...... 121
Installment Options and Static Hedging Mark H. A. Davis, Walter Schachermayer and Robert G. Tompkins ...... 131
Fractional Brownian Motion and Financial Modelling R.J. Elliott and J. van der Hoek ...... 140
Stochastic Volatility and Epsilon-Martingale Decomposition Jean-Pierre Fouque, George Papanicolaou and Ronnie Sircar ...... 152
Mutual Debts Compensation as Graph Theory Problem Vladimir Gazda ...... 162
First Steps to Stochastic Finance Hans-Joachim Girlich ...... 168
Fractional Calculus and Continuous-Time Finance III: the Diffusion Limit Rudolf Gorenflo, Francesco Mainardi, Enrico Scalas and Marco Raberto .... 171
Passport Options Outside the Black Scholes World Vicky Henderson ...... 181
New Developments in Backward Stochastic Riccati Equations and Their Applications Michael Kohlmann and Shanjian Tang ...... 194
Quantile hedging for a jump-diffusion financial market model R.N.Krutchenko and A.V.Melnikov ...... 215
Exponential formula and Girsanov theorem for mixed semilinear stochastic differential equations Yuriy Krvavych and Yuliya Mishura ...... 230
An introduction to optimal consumption with partial observation D. Lefevre, B. 0ksendal, and Agnes Sulem ...... 239 Table of Contents 9
Continuous Time CAPM, Price for Risk and Utility Maximization Johannes Leitner ...... 250
LQ control and mean-variance portfolio selections: The stochastic parameter case Andrew E.B. Lim and Xun Yu Zhou ...... 261
Liquidity Risk in Energy Markets S.Nagornii and G.Dozeman ...... 271
Riccati Equation and Viscosity Solutions in Mean Variance Hedging Bernhard Peisl ...... 283
A Minimal Financial Market Model Eckhard Platen ...... 293
A note on equivalent martingale measures with bounded density Miklos Rasonyi ...... 302
Local optimality in the multi-dimensional multi-period mean-variance portfolio problem Manfred Schiil ...... 307
Transaction Processes among Autonomous Traders Julia Schmelz ...... 317
The Laplace transform approach to valuing exotic options: the case of the Asian option Michael Schroder ...... 328
Reversible Real Options Mark Shackleton and Rafal Wojakowski ...... 339
A Toolbox for Generalized Relative Entropies, EMM and Contingent Claim Valuation Wolfgang Stummer ...... 345
Incremental Value-at-Risk: traps and misinterpretations Luisa Tibiletti ...... 355
On option expected returns Rafa} Wojakowski and Mark Shackleton ...... 365 Participants workshop on mathematical finance, Konstanz, October 5-7, 2000
Volbert Alexander University of Giessen, Giessen, Germany
J.S.F Barbachan Universidade Catolica de Braslia, Brasilia, Brazil [email protected]
Juergen W. Bauer Germany Dr.J uergen W [email protected]
Christian Bender University of Konstanz, Konstanz, Germany christian. [email protected]
Fred Espen Benth University of Oslo, Oslo, Norway [email protected]
Francesca Biagini University of Bologna, Bologna, Italy [email protected]
Frederik Boetius University of Konstanz, Konstanz, Germany frederik. [email protected]
Anton Buchmeier Siemens AG, Munchen, Germany anton. [email protected]
Volker Burkel University of Konstanz, Konstanz, Germany volker. [email protected] 12 workshop on mathematical finance, Konstanz, October 5-7, 2000
Mark Davis Imperial College, London, UK [email protected]
Karim Djaidja University of Konstanz, Konstanz, Germany
Thomas Domenig Ziircher Kantonalbank, Zurich, Switzerland
G. Dozeman SEE, Amstelveen, The Netherlands
Dana Diivelmeyer TU Chemnitz, Chemnitz, Germany [email protected]
Nicole EI Karoui Poly technique Paris,Paris,France [email protected]
Robert Elliott UAlta, Edmonton, Edmonton, Canada r [email protected]
Jean-Pierre Fouque North Carolina State University, Raleigh, USA [email protected]
Riidiger Frey University of Zuerich, Zuerich, Switzerland [email protected]
Vladimir Gazda University of Bratislava, Bratislava, Slovakia [email protected]
Hans-Joachim Girlich University of Leipzig, Leipzig, Germany [email protected] workshop on mathematical finance, Konstanz, October 5-7, 2000 13
Rudolf Gorenflo Free University of Berlin, Berlin, Germany [email protected]
Peter Grandits TU Wien, Wien, Austria [email protected]
Emmanuel Haven Concordia University, Cote St. Luc, Canada [email protected]
Vicky Henderson University of Warwick, Warwick,UK [email protected]
Juri Hinz University of Tuebingen, Tuebingen, Germany [email protected]
Markus Chr. Holder HSBC Trinkaus und Burkhardt KGaA [email protected]
Ralf Jager University of Marburg, Marburg, Germany [email protected]
Jan Kallsen Universtity of Freiburg, Freiburg i. Br., Germany [email protected]
Anne Kandler TU Chemnitz, Chemnitz, Germany [email protected]
Ioannis Karatzas Columbia University, New York, USA [email protected]
Moritz Kassmann University of Bonn, Bonn, Germany 14 workshop on mathematical finance, Konstanz, October 5-7, 2000
Claudia Kliippelberg TU Muenchen, Muenchen, Germany [email protected]
Marek Kocinski Warsaw Agricultural University, Warsaw, Poland [email protected]
Michael Kohlmann University of Konstanz, Konstanz, Germany [email protected]
Christoph Krischanitz UNIQA Versicherungen AG, Wien, Austria [email protected]
K. Suresh Kumar University of Twente, Enschede, Netherlands
Yuriy Krvavych Kyiv University, Kyiv, Ukraine [email protected]
LanYun Lao Fudan University, Shanghai, China [email protected]
Johannes Leitner University of Konstanz, Konstanz, Germany [email protected]
Serguei Levendorski Rostov State University, Rostov-on-Don, Russia [email protected]
Andrew Lim Columbia University, New York,USA [email protected]
Karsten Linowsky workshop on mathematical finance, Konstanz, October 5-7, 2000 15
Arne Lokka University of Oslo, Oslo, Norway [email protected]
Enrico Melchioni FMR Consulting, Voghera, Italy [email protected]
A.V. Melnikov Steklov Institute, Moscow, Russia [email protected]
Leonid Mytnik Technion, Israel Institute of Technology, Technion City, Haifa, Israel [email protected]
Sergey Nagornii, SEE [email protected]
Bernt Oeksendal University of Oslo, Oslo, Norway [email protected]
Andrea Pallavicini FMR Consulting, Voghera, Italy [email protected]
Bernhard Peisl University of Konstanz, Konstanz, Germany bernhard. [email protected]
Eckhard Platen University of Technology, Sydney, Australia eckhard. [email protected]
Stanley Pliska University of Illinois Chicago, Chicago, USA [email protected]
Miklos Rasonyi University of Budapest, Budapest, Hungary [email protected] 16 workshop on mathematical finance, Konstanz, October 5-7, 2000
Paul Ressel University of Eichstaett, Eichstaett, Germany [email protected]
Wolfgang Runggaldier University of Padova, Padova, Italy [email protected]
Joern Sass University of Kiel, Kiel, Germany
M. Schill University of Bonn, Bonn, Germany [email protected]
Julia Schmelz TU Muenchen, Muenchen, Germany [email protected]
Thorsten Schmidt University of GieBen, GieBen, Germany [email protected]
Stefan Scholz
Michael Schroeder University of Mannheim, Mannheim, Germany [email protected]
Martin Schweizer TU Berlin, Berlin, Germany [email protected]
Mark Shackleton Lancaster University, Lancaster, UK [email protected]
Mikhail Soloveitchik Dresdner Bank, Germany [email protected] [email protected] workshop on mathematical finance, Konstanz, October 5-7, 2000 17
Thomas Sparla University of Dortmund, Dortmund, Germany [email protected]
Srdjan Stojanovic University of Cincinnati, Cincinnati, OH, USA [email protected]
Wolfgang Stummer University of VIm, VIm, Germany [email protected]
W. Stute University of Siegen, Siegen, Germany [email protected]
Barbara Swart University of Pretoria, Pretoria, South Africa [email protected]
Shanjian Tang Fudan University, Shanghai, China [email protected]
Dirk Tasche Munich University of Technology, Muenchen, Germany [email protected]
Luisa Tibiletti University of Torino, Torino, Italy [email protected]
Tiziano Vargiolu University of Padova, Padova, Italy [email protected]
O. Weick University of Freiburg, Freiburg, Germany [email protected]
Ralf Wilke University of Dortmund, Dortmund, Germany wilke@statistik. uni-dortmund. de 18 workshop on mathematical finance, Konstanz, October 5-7,2000
Rafal Wojakowski Lancaster University, Lancaster, UK [email protected]
Uwe Wystup Commerzbank, Frankfurt, Germany [email protected]
Aleksandar Zatezalo Siemens AG, Mnchen, Germany [email protected]
Xuelei Zhao Fudan University, Shanghai, China [email protected]
X.Y. Zhou CUHK, Hong Kong, China
Helmut Zink University of Berne, Berne, Switzerland