Discretisation of stochastic control problems for continuous time dynamics with delay

https://doi.org/10.1016/j.cam.2006.02.062Get rights and content
Under an Elsevier user license
open archive

Abstract

As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow for delay in the dynamics. The existence of an optimal strategy with respect to the cost functional can be guaranteed in the class of relaxed controls. Weak convergence of the approximating extended Markov chains to the original process together with convergence of the associated optimal strategies is established.

MSC

93E20
34K50
60H35

Keywords

Stochastic delay differential equations
Stochastic optimal control
Finite-difference approximation

Cited by (0)

Financial support by the DFG-Sonderforschungsbereich 649 Economic Risk is gratefully acknowledged.