Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time

Asgar Jamneshan, Michael Kupper, José Miguel Zapata-García
2020 Journal of Optimization Theory and Applications  
We prove a general existence result in stochastic optimal control in discrete time, where controls, taking values in conditional metric spaces, depend on the current information and past decisions. The general form of the problem lies beyond the scope of standard techniques in stochastic control theory, the main novelty is a formalization in conditional metric space and the use of conditional analysis. We illustrate the existence result by several examples such as wealth-dependent utility
more » ... zation under risk constraints and utility maximization with a conditional dimension. We also provide a discussion as to how our methods compare to techniques based on random sets.
doi:10.1007/s10957-020-01711-z fatcat:k5gbvtc4cvg4xohr6qly5u6rpe