The existence of optimal feedback controls for stochastic dynamical systems with regime-switching

2019/06/20 by Shao, Jinghai
#49K30 #60J27 #60J60 #93B52 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.1906.08425

Abstract

In this work we provide explicit conditions on the existence of optimal feedback controls for stochastic processes with regime-switching. We use the compactification method which needs less regularity conditions on the coefficients of the studied stochastic systems. Two different kinds of controls have been considered: one is the control on the coefficients of the diffusion processes, another is the control on the transition rate matrices of the continuous-time Markov chains. Moreover, the dynamic programming principle is established after showing the continuity of the value function.

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