Discretisation of stochastic control problems for continuous time dynamics with delay - Markus Fischer; Markus Reiß (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2005)
As a main step in the numerical solution of control problems in continous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretizing 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.
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