Applications of Variational Inequalities in Stochastic Control

Alain Bensoussan and Jacques-Louis Lions (Eds.)9780080875330, 9780444863584, 0444863583

This book treats second order partial differential equations and unilateral problems, as well as stochastic control and optimal stopping-time problems. It deals with branches of mathematics which r.ay at first sight appear totally different and which have developed along quite independent lines, but which are in fact strongly inter-related and which are capable of cross-fertilising each other. The fundamental link lies in the interpretation of the solutions of certain partial differential equations. This interpretation is an extension of the method of characteristics which allows the solution of a linear first-order hyperbolic equation to be expressed explicitly as a functional defined along the characteristic trajectories. A similar phenomenon arises in the case of parabolic or elliptic equations, but the characteristic trajectories then become stochastic processes. In very general terms, it is absolutely necessary to resort to probabilistic models if we wish to be able to give explicit formulas for the solutions of partial differential equations (or of systems of.such equations).

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Table of contents :
Content:
Editors
Page ii

Edited by
Page iii

Copyright page
Page iv

Foreword
Pages v-vi

Chapter 1 General Introduction to Optimal Stopping Time Problems
Pages 1-20

Chapter 2 Stochastic Differential Equations and Linear Partial Differential Equations of Second Order
Pages 21-186

Chapter 3 Optimal Stopping-Time Problems and Variational Inequalities
Pages 187-493

Chapter 4 Stopping-Time and Stochastic Optimal Control Problems
Pages 495-557

Bibliography
Pages 559-564