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

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...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2024, Vol.47 (1), Article 34
Main Authors: Ben-Gherbal, Hanane, Mezerdi, Brahim
Format: Article
Language:English
Subjects:
Applications of Mathematics
Compensators
Differential equations
Mathematics
Mathematics and Statistics
Maximum principle
Optimal control
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Summary: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.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-023-01632-w