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Methods of Mathematical Finance

Ioannis Karatzas, Steven E. Shreve
3rd Edition
New York: Springer, 2001
422pp, ISBN: 978-0-387-94839-3

This technical exploration of mathematical finance methods presents techniques of practical importance, as well as advanced methods for research. It focuses on applications of stochastic analysis and optimal control theory to various problems, and provides analysis of portfolio optimization and valuation problems under constraints, as well as contingent claim pricing and optimal consumption/investment in both complete and incomplete markets.

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Methods of Mathematical Finance (Stochastic Modelling and Applied Probability)

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Product Description

This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

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