→ Elementary Stochastic Calculus With Finance in View

Description: 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.

Table of Contents Reader Guidelines 1 1 Preliminaries 5 2 The Stochastic Integral 87 3 Stochastic Differential Equations 131 4 Applications of Stochastic Calculus in Finance 167 App. A1 Modes of Convergence 185 App. A2 Inequalities 187 App. A3 Non-Differentiability and Unbounded Variation of Brownian Sample Paths 188 App. A4 Proof of the Existence of the General Ito Stochastic Integral 190 App. A5 The Radon-Nikodym Theorem 193 App. A6 Proof of the Existence and Uniqueness of the Conditional Expectation 194 Bibliography 195 Index 199 List of Abbreviations and Symbols 209