Translations of Mathematical Monographs
1999; 133 pp; Hardcover
MSC: Primary 90; Secondary 60
Print ISBN: 978-0-8218-1082-8
Product Code: MMONO/184
List Price: $78.00
Individual Member Price: $62.40
Financial Markets: Stochastic Analysis and the Pricing of Derivative SecuritiesShare this page
A. V. Mel′nikov
Financial mathematics is going through a period of intensive
development, particularly in the area of stochastic analysis. This
timely work presents a comprehensive, self-contained 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 Black-Scholes 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.
Table of Contents
Table of Contents
Financial Markets: Stochastic Analysis and the Pricing of Derivative Securities
Graduate students and researchers working in probability theory, stochastic processes, and financial mathematics.
The book provides a rigorous, self-contained 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