Stochastic control for Backward Stochastic Differential Equations with semi-Markov chain noises
Abstract
In this paper, we extend the results of Elliott and Yang elliott3 and discuss the control of a stochastic process for which the driving noise is provided by a martingale associated with a semi-Markov Chain. An existence and a comparison theorem are obtained. In our discrete time setting, adjoint processes are provided by backward stochastic difference equations. Technical results from partial differential equation theory to establish a verification theorem are not required.
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