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.

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

"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."

"... 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."