Mathematical Finance

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.

Klappentext

The year 2000 is the centenary year of the publication of Bachelier's thesis which - together with Harry Markovitz Ph.D. dissertation on portfolio selection in 1952 and Fischer Black's and Myron Scholes' solution of an option pricing problem in 1973 - is considered as the starting point of modern finance as a mathematical discipline. On this remarkable anniversary the workshop on mathematical finance held at the University of Konstanz brought together practitioners, economists and mathematicians to discuss the state of the art. Apart from contributions to the known discrete, Brownian, and Lévy process models, first attempts to describe a market in a reasonable way by a fractional Brownian motion model are presented, opening many new aspects for practitioners and new problems for mathematicians. As most dynamical financial problems are stochastic filtering or control problems many talks presented adaptations of control methods and techniques to the classical financial problems in . portfolio selection . irreversible investment . risk sensitive asset allocation . capital asset pricing . hedging contingent claims . option pricing . interest rate theory. The contributions of practitioners link the theoretical results to the steadily increasing flow of real world problems from financial institutions into mathematical laboratories. The present volume reflects this exchange of theoretical and applied results, methods and techniques that made the workshop a fruitful contribution to the interdisciplinary work in mathematical finance.

Inhalt
Note: in the titles of co-authored papers the lecturer's name is in bold face).- Preface.- Participants.- On-line portfolio strategy with prediction.- Continuous time financial market, transaction cost and transaction intensity.- Demand Heterogeneity and Price Volatility.- Optimal default boundary in a discrete time setting.- An Infinite Factor Model for the Interest Rate Derivatives.- Arbitrage and Pricing with Collateral.- On the existence of optimal controls for a singular stochastic control problem in finance.- A Quadratic Approach To Interest Rates Models In Incomplete Markets.- Risk Sensitive Asset Management: Two Empirical Examples.- Bounded Variation Singular Stochastic Control and Associated Dynkin Game.- Option Pricing and Hedging Under Regular Lévy Processes of Exponential Type.- Installment Options and Static Hedging.- Fractional Brownian Motion and Financial Modelling.- Stochastic Volatility and Epsilon-Martingale Decomposition.- Mutual Debts Compensation as Graph Theory Problem.- First Steps to Stochastic Finance.- Fractional Calculus and Continuous-Time Finance III: the Diffusion Limit.- Passport Options Outside the Black Scholes World.- New Developments in Backward Stochastic Riccati Equations and Their Applications.- Quantile hedging for a jump-diffusion financial market model.- Exponential formula and Girsanov theorem for mixed semilinear stochastic differential equations.- An introduction to optimal consumption with partial observation.- Continuous Time CAPM, Price for Risk and Utility Maximization.- LQ control and meanvariance portfolio selections: The stochastic parameter case.- Liquidity Risk in Energy Markets.- Riccati Equation and Viscosity Solutions in Mean Variance Hedging.- A Minimal Financial Market Model.- A note on equivalentmartingale measures with bounded density.- Local optimality in the multi-dimensional multi-period mean-variance portfolio problem.- Transaction Processes among Autonomous Traders.- The Laplace transform approach to valuing exotic options: the case of the Asian option.- Reversible Real Options.- A Toolbox for Generalized Relative Entropies, EMM and Contingent Claim Valuation.- Incremental Value-at-Risk: traps and misinterpretations.- On option expected returns.