Controlled Diffusion Processes

ISBN-13: 9783540709138 / Angielski / Miękka / 2008 / 310 str.

N. V. Krylov; A. B. Aries

Opis

This book covers the optimal control of solutions of fully observable Ito-type stochastic differential equations. It proves the validity of the Bellman differential equation for payoff functions and develops rules for optimal control strategies.

Recenzje

From the reviews:

"The book treats a large class of fully nonlinear parabolic PDEs via probabilistic methods. ... The monograph may be strongly recommended as an excellent reading to PhD students, postdocs et al working in the area of controlled stochastic processes and/or nonlinear partial differential equations of the second order. ... recommended to a wider audience of all students specializing in stochastic analysis or stochastic finance starting from MSc level." (Alexander Yu Veretennikov, Zentralblatt MATH, Vol. 1171, 2009)

Spis treści

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.

Blurb

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 L_p-estimates of stochastic integral distributions; the existence theorem for stochastic equations; the Itô formula for functions; and the Bellman principle, equation, and normalized equation.