This book deals with the optimal control of solutions of fully observable Itô-type stochastic differential equations. The validity of the Bellman differential equation for payoff functions is proved and rules for optimal control strategies are developed.
Topics include optimal stopping; one dimensional controlled diffusion; the Lp-estimates of stochastic integral distributions; the existence theorem for stochastic equations; the Itô formula for functions; and the Bellman principle, equation, and normalized equation.
Author(s): Nicolai V. Krylov (auth.)
Series: Stochastic Modelling and Applied Probability 14
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1980
Language: English
Pages: 310
Tags: Probability Theory and Stochastic Processes
Front Matter....Pages i-xii
Introduction to the Theory of Controlled Diffusion Processes....Pages 1-43
Auxiliary Propositions....Pages 45-128
General Properties of a Payoff Function....Pages 129-161
The Bellman Equation....Pages 163-211
The Construction of ε -Optimal Strategies....Pages 213-243
Controlled Processes with Unbounded Coefficients: The Normed Bellman Equation....Pages 245-292
Back Matter....Pages 293-308
