Synopses & Reviews
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.
Review
"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)
Synopsis
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.
Synopsis
This book is intended for readers who are quite familiar with probability and stochastic processes but know little or nothing about ?nance. It is written in the de?nition/theorem/proof style of modern mathematics and attempts to explain as much of the ?nance motivation and terminology as possible. A mathematical monograph on ?nance can be written today only - cause of two revolutions that have taken place on Wall Street in the latter half of the twentieth century. Both these revolutions began at universities, albeit in economics departments and business schools, not in departments of mathematicsor statistics. Theyhaveledinexorably, however, to anes- lation in the level of mathematics (including probability, statistics, partial di?erential equations and their numerical analysis) used in ?nance, to a point where genuine research problems in the former ?elds are now deeply intertwined with the theory and practice of the latter. The ?rst revolution in ?nance began with the 1952 publication of Po- folio Selection, an early version of the doctoral dissertation of Harry Markowitz. This publication began a shift away from the concept of t- ing to identify the best stock for an investor, and towards the concept of trying to understand and quantify the trade-o's between risk and - turn inherent in an entire portfolio of stocks. The vehicle for this so-called mean variance analysis of portfolios is linear regression; once this analysis is complete, one can then address the optimization problem of choosing the portfolio with the largest mean return, subject to keeping the risk (i. e."
Table of Contents
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