Translations of Mathematical Monographs 1999; 133 pp; hardcover Volume: 184 ISBN10: 0821810820 ISBN13: 9780821810828 List Price: US$78 Member Price: US$62.40 Order Code: MMONO/184
 Financial mathematics is going through a period of intensive development, particularly in the area of stochastic analysis. This timely work presents a comprehensive, selfcontained introduction to stochastic financial mathematics. It is based on lectures given at Moscow State University, "Stochastic Analysis in Finance", and comprises the basic methods and key results of the theory of derivative securities pricing in discrete financial markets. The following elements: martingales, semimartingales, stochastic exponents, Itô's formula, Girsanov's theorem, and more, are used to characterize notions such as arbitrage and completeness of financial markets, fair price and hedging strategies for options, forward and futures pricing, and utility maximization. Limiting transition from a discrete to continuous model with derivation of the famous BlackScholes formula is shown. The book contains a wide spectrum of material and can serve as a bridge to continuous models. It is suitable as a text for graduate and advanced graduate students studying economics and/or financial mathematics. Readership Graduate students and researchers working in probability theory, stochastic processes, and financial mathematics. Reviews "The book provides a rigorous, selfcontained and concise introduction to the rapidly developing field of mathematical finance. It may serve very well as a textbook for graduate students in mathematics or finance."  Mathematical Reviews "The book is carefully written and contains a short but clear introduction to the theory of stochastic modelling of financial markets. It could be highly recommended as an introductory course to the topic for graduate students and specialists interested in financial mathematic problems."  Zentralblatt MATH Table of Contents  Basic concepts and objects of a financial market
 The elements of discrete stochastic analysis
 A stochastic model for a financial market. Arbitrage and completeness
 Pricing European options in complete markets. The binomial model and the CoxRossRubinstein formula
 Pricing and hedging American options in complete markets
 Financial computations on a complete market with the use of nonselffinancing strategies
 Incomplete markets. Pricing of options and problems of minimizing risk
 The structure of prices of other instruments of a financial market. Forwards, futures, bonds
 The problem of optimal investment
 The concept of continuous models. Limiting transitions from a discrete market to a continuous one. The BlackScholes formula
 Appendix 1
 Appendix 2
 Appendix 3
 Hints for solving the problems
 Bibliography
 Subject index
