Ioannis Karatzas
Departments of Mathematics
and Statistics
Columbia University

Steven E. Shreve
Department of Mathematical Sciences
Carnegie Mellon University

Stochastic Modelling and Applied Probability

Marek RutKowski, Mathematical Reviews

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."

About this book
Written by two of the best-known researchers in mathematical finance, this book presents techniques of practical importance as well as advanced methods for research. Contingent claim pricing and optimal consumption/investment in both complete and incomplete markets are discussed, as well as Brownian motion in financial markets and constrained consumption and investment. This book treats these topics in a unified manner and is of practical importance to practitioners in mathematical finance, especially for pricing exotic options.
Written for:
Researchers, practitioners, graduate students