**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 Securities

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*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

#### Readership

Graduate students and researchers working in probability theory, stochastic processes, and financial mathematics.

#### Reviews

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