Modelling with the It?? 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 It?? 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 It?? Integral; The It?? Lemma; The Stratonovich and Other Integrals; Stochastic Differential Equations: Deterministic Differential Equations; It?? 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 It?? Stochastic Integral; The Radon Nikodym Theorem; Proof of the Existence and Uniqueness of the Conditional Expectation.