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Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time

Author

Listed:
  • Asgar Jamneshan

    (UCLA)

  • Michael Kupper

    (University of Konstanz)

  • José Miguel Zapata-García

    (University of Konstanz)

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.

Suggested Citation

  • Asgar Jamneshan & Michael Kupper & José Miguel Zapata-García, 2020. "Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 644-666, August.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:2:d:10.1007_s10957-020-01711-z
    DOI: 10.1007/s10957-020-01711-z
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    References listed on IDEAS

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    Cited by:

    1. Antonio Avilés López & José Miguel Zapata García, 2020. "Boolean Valued Representation of Random Sets and Markov Kernels with Application to Large Deviations," Mathematics, MDPI, vol. 8(10), pages 1-23, October.

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