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This book is the sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion-driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. 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 researchpapers, 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 equilbrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation presents techniques of practical importance, especially for pricing exotic options.
List of contents
A Brownian Motion of Financial Markets.
- Contingent Claim Valuation in aComplete Market.
- Single-Agent Consumption and Investment.
- Equilibrium in a Complete Market.
- Contingent Claims in Incomplete Markets.
- Constrained Consumption and Investment.
Report
"The book under review deals with the applications of stochastic analysis and optimal control theory to various problems arising in modern mathematical finance. In contrast to several other books on mathematical finance which appeared in recent years, this book deals not only with the so-called partial equilibrium approach (i.e., the arbitrage pricing of European and American contingent claims) but also with the general equilibrium approach (i.e., with the equilibrium specification of prices of primary assets). A major part of the book is devoted to solving valuation and portfolio optimization problems under market imperfections, such as market incompleteness and portfolio constraints. ... Undoubtedly, the book constitutes a valuable research-level text which should be consulted by anyone interested in the area. Unlike other currently available monographs, it provides an exhaustive and up-to-date treatment of portfolio optimization and valuation problems under constraints. It is also quite suitable as a textbook for an advanced course on mathematical finance." (Marek RutKowski, Mathematical Reviews)
