Stochastic Calculus for Finance - Capi¿ski, Marek

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Résumé :
This book introduces key results essential for financial practitioners by means of concrete examples and a fully rigorous exposition.

Biographie:
Marek Capi?ski has published over fifty research papers and nine books. His diverse interests include mathematical finance, corporate finance and stochastic hydrodynamics. For over thirty-five years he has been teaching these topics, mainly in Poland and in the UK, where he has held visiting fellowships. He is currently Professor of Applied Mathematics at AGH University of Science and Technology in Krakow, where he established a Master's programme in mathematical finance.

Sommaire:
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 It? 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 It? 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 It? 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....