A Brownian Motion of Financial Markets * Contingent Claim Valuation in a Complete Market * Single-Agent Consumption and Investment * Equilibrium in a Complete Market * Contingent Claims in Incomplete Markets * Constrained Consumption and Investment
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.
Written by two of the best-known researchers in mathematical finance, this book will appeal to theorists and practitioners in this very active research area. It includes much material that has not appeared before in book-form.