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The Relaxed Stochastic Maximum Principle in Singular Optimal Control of Jump Diffusions

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Abstract

This paper deals with optimal control of systems driven by stochastic differential equations (SDEs), with controlled jumps, where the control variable has two components, the first being absolutely continuous and the second singular. We study the corresponding relaxed-singular problem, in which the first part of the admissible control is a measure-valued process and the state variable is governed by a SDE driven by a relaxed Poisson random measure, whose compensator is a product measure. We establish a stochastic maximum principle for this type of relaxed control problems extending existing results. The proofs are based on Ekeland’s variational principle and stability properties of the state process and adjoint variable with respect to the control variable.

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Acknowledgements

The second author would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum and Minerals, KSA (KFUPM), for funding this work through Project No: SB201017. The authors would like to thank the anonymous referee for useful and helpful comments, which lead to a substantial improvement of our paper.

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Authors and Affiliations

  1. Department of Exact Sciences, École Normale Supérieure de Ouargla, BP 398, Hai Ennasr, 30000, Ouargla, Algeria

    Hanane Ben-Gherbal

  2. Department of Mathematics, King Fahd University of Petroleum and Minerals, P.O. Box 1916, 31261, Dhahran, Saudi Arabia

    Brahim Mezerdi

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  1. Hanane Ben-Gherbal
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  2. Brahim Mezerdi
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Correspondence to Brahim Mezerdi.

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Communicated by Rosihan M. Ali.

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Ben-Gherbal, H., Mezerdi, B. The Relaxed Stochastic Maximum Principle in Singular Optimal Control of Jump Diffusions. Bull. Malays. Math. Sci. Soc. 47, 34 (2024). https://doi.org/10.1007/s40840-023-01632-w

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  • DOI: https://doi.org/10.1007/s40840-023-01632-w

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