Stochastic Calculus for Finance

Marek Capiński; Ekkehard Kopp; Janusz Traple

doi:10.1017/CBO9781139017367

This book focuses specifically on the key results in stochastic processes that have become essential for finance practitioners to understand. The authors study the Wiener process and Itô integrals in some detail, with a focus on results needed for the Black–Scholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Itô formula (proved in detail) become the centrepiece, both for theory and applications, and to provide concrete examples of stochastic differential equations used in finance. Finally, proofs of the existence, uniqueness and the Markov property of solutions of (general) stochastic equations complete the book. Using careful exposition and detailed proofs, this book is a far more accessible introduction to Itô calculus than most texts. Students, practitioners and researchers will benefit from its rigorous, but unfussy, approach to technical issues. Solutions to the exercises are available online.

'… a very accessible and comprehensive introduction.'

Robert Stelzer Source: Mathematical Reviews

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-viii
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1 - Discrete-time processes
pp 1-35
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2 - Wiener process
pp 36-77
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3 - Stochastic integrals
pp 78-108
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4 - Itô formula
pp 109-151
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5 - Stochastic differential equations
pp 152-175
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Index
pp 176-177
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Stochastic Calculus for Finance

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

1 - Discrete-time processes
pp 1-35

2 - Wiener process
pp 36-77

3 - Stochastic integrals
pp 78-108

4 - Itô formula
pp 109-151

5 - Stochastic differential equations
pp 152-175

Index
pp 176-177

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Stochastic Calculus for Finance

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