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Participants Workshop on Mathematical Finance, Konstanz, October 5-7, 2000 TRENDS IN MATHEMATICS Trends in Mathematics is a series devoted to the publication of volumes arising from conferences and lecture series focusing on a particular topic from any area of mathematics. Its aim is to make current developments available to the community as rapidly as possible without compromise to quality and to archive these for reference. Proposals for volumes can be sent to the Mathematics Editor at either Birkhäuser Verlag P.O. Box 133 CH-4010 Basel Switzerland or Birkhäuser Boston Inc. 675 Massachusetts Avenue Cambridge, MA 02139 USA Material submitted for publication must be screened and prepared as follows: All contributions should undergo a reviewing process similar to that carried out by journals and be checked for correct use of language which, as a rule, is English. Articles without proofs, or which do not contain any significantly new results, should be rejected. High quality survey papers, however, are welcome. We expect the organizers to deliver manuscripts in a form that is essentially ready for direct reproduction. Any version of TEX is acceptable, but the entire collection of files must be in one particular dialect of TEX and unified according to simple instructions available from Birkhäuser. Furthermore, in order to guarantee the timely appearance of the proceedings it is essential that the final version of the entire material be submitted no later than one year after the con• ference. The total number of pages should not exceed 350. The first-mentioned author of each article will receive 25 free offprints. To the participants of the congress the book will be offered at a special rate. Mathematical Finance Workshop of the Mathematical Finance Research Project, Konstanz, Germany, October 5-7, 2000 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 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is con• cerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 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 ...................................
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