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We prove a general existence result in stochastic optimal control in discretetime where controls take values in conditional metric spaces, and depend on thecurrent state and the information of past decisions through the evolution of arecursively defined forward process. The generality of the problem lies beyondthe scope of standard techniques in stochastic control theory such as randomsets, normal integrands and measurable selection theory. The main novelty is aformalization in conditional metric space and the use of techniques inconditional analysis. We illustrate the existence result by several examplesincluding wealth-dependent utility maximization under risk constraints withbounded and unbounded wealth-dependent control sets, utility maximization witha measurable dimension, and dynamic risk sharing. Finally, we discuss howconditional analysis relates to random set theory.

Parameter-dependent Stochastic Optimal Control in Finite Discrete Time