ELEMENTARY STOCHASTIC CALCULUS WITH FINANCE IN VIEW MIKOSCH T. Księgarnia

Modelling with the Itô integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory.

This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black-Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Itô calculus and/or stochastic finance.

Table of Contents:

Preliminaries:

Basic Concepts from Probability Theory

Stochastic Processes

Brownian Motion

Conditional Expectation

Martingales

The Stochastic Integral:

The Riemann and Riemann-Stieltjes Integrals

The Itô Integral

The Itô Lemma

The Stratonovich and Other Integrals

Stochastic Differential Equations:

Deterministic Differential Equations

Itô Stochastic Differential Equations

The General Linear Differential Equation

Numerical Solution

Applications of Stochastic Calculus in Finance:

The Black-Scholes Option-Pricing Formula

A Useful Technique: Change of Measure

Appendices:

Modes of Convergence

Inequalities

Non-Differentiability and Unbounded Variation of Brownian Sample Paths

Proof of the Existence of the General Itô Stochastic Integral

The Radon-Nikodym Theorem

Proof of the Existence and Uniqueness of the Conditional Expectation

Readership: Economists, financial engineers, mathematicians and physicists.

"This book under review can be determined as a very successful work ... the author's choice of the material is done with good taste and expertise ... It can be strongly recommended to graduate students and practitioners in the field of finance and economics." Mathematics Abstracts, 2000

"... this is a well-written book, which makes the difficult object of mathematical finance easy to understand also for non-mathematicians. It might be useful for economics students and all practitioners in the field of finance who are interested in the mathematical methodology behind the Black-Scholes model." Statistical Papers, 2000

212 pages

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