Description

Book Synopsis
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 Ità integrals in some detail, with a focus on results needed for the BlackâScholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Ità 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 Ità 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.

Trade Review
'… a very accessible and comprehensive introduction.' Robert Stelzer, Mathematical Reviews

Table of Contents
Preface; 1. Discrete time processes; 2. Wiener process; 3. Stochastic integrals; 4. Itô formula; 5. Stochastic differential equations; Index.

Stochastic Calculus for Finance Mastering Mathematical Finance

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    A Paperback by Marek CapiÅ„ski, Ekkehard Kopp, Janusz Traple

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      Book details

      Publisher Cambridge University Press
      Published 8/23/2012 12:00:00 AM
      ISBN-13 9780521175739
      978-0521175739
      ISBN-10 0521175739
      Also in:
      Applied mathematics

      Description

      Book Synopsis
      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 Ità integrals in some detail, with a focus on results needed for the BlackâScholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Ità 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 Ità 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.

      Trade Review
      '… a very accessible and comprehensive introduction.' Robert Stelzer, Mathematical Reviews

      Table of Contents
      Preface; 1. Discrete time processes; 2. Wiener process; 3. Stochastic integrals; 4. Itô formula; 5. Stochastic differential equations; Index.

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