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

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1. Ebooks list page : 2941
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