This book deals with the optimal control of solutions of fully observable Itรด-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 Itรด formula for functions; and the Bellman principle, equation, and normalized equation
CONTENT
to the Theory of Controlled Diffusion Processes -- Auxiliary Propositions -- General Properties of a Payoff Function -- The Bellman Equation -- The Construction of ?-Optimal Strategies -- Controlled Processes with Unbounded Coefficients: The Normed Bellman Equation
