ARBITRAGE THEORY IN CONINUOUS TIME BJORK T Księgarnia

Tomas Bjork is Professor of Mathematical Finance at the Stockholm School of Economics. His background is in probability, and he has previously been Associate Professor of Mathematics at the Royal Institute of Technology in Stockholm. He is a member of the editorial board of the journal Finance and Stochastics, published by Springer Verlag.

This book gives a comprehensive account of the arbitrage theory of financial derivatives in a mathematically precise way, but without the explicit use of abstract measure theory. It is aimed at graduate students and practitioners in economics, but will also be of interest to mathematicians and researchers in finance. The text is heavily orientated towards concrete computations and practical handling of stochastic differential equations, in their economic applications as well as in their purely mathematical context. The reader will find numerous worked-out examples as well as a large number of exercises.

After an introductory chapter on the binomial model, the focus is exclusively on continuous time models. The reader is given a self-contained treatment of stochastic differential equations and Ito calculus, including the Feynman-Kac connections to partial differential equations, and the classical Kolmogorov equations.

The methodological approach to arbitrage pricing is taken through the use and construction of locally riskless portfolios. This leads immediately to pricing formulas as solutions to partial differential equations. Risk neutral valuation formulas and martingale measures are then introduced through Feynman-Kac representations of the solutions of the PDEs. Still, the text is essentially a probabilistic one, emphasizing the use of martingale measures for the computation of prices. The book covers stock price models, with one or several underlying assets, and presents a full treatment of both pricing and hedging. A special chapter is devoted to pricing and hedging problems in incomplete models. Barrier options, options on dividend-paying assets, as well as currency markets (including quanto products) are given separate chapters.

Interest rate theory is dealt with in some depth, including the most common short rate models, affine term structures, inversion of the yield curve, and the Heath-Jarrow-Morton approach to forward rate models. A separate chapter is devoted to the modern change-of-numeraire technique, which makes it possible to give concrete pricing formulas for a large number of fairly complicated interest rate derivatives.

The book also includes a self-contained treatment of stochastic optimal control theory, on the fringes of arbitrage pricing, but of interest to the general reader. This theory is then applied to optimal consumption/ investment problems, and the Merton fund separation theorems are derived.

311 pages

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