Publication: Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time
Authors
Jamneshan, Asgar ; Kupper, Michael ; Zapata García, José Miguel
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Publisher
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DOI
https://doi.org/10.1007/s10957-020-01711-z
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info:eu-repo/semantics/article
Description
© 2020, The Author(s). This manuscript version is made available under the CC-BY 4.0 license http://creativecommons.org/licenses/by/4.0/. This document is the Published version of a Published Work that appeared in final form in Journal of Optimization Theory and Applications. To access the final edited and published work see https://doi.org/10.1007/s10957-020-01711-z
Abstract
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 maximization 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.
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Citation
Journal of Optimization Theory and Applications (2020) 186:644–666
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