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Mathematics > Optimization and Control

arXiv:2210.01197 (math)
[Submitted on 3 Oct 2022]

Title:Maximum principle for discrete time mean-field stochastic optimal control problems

Authors:Arzu Ahmadova, Nazim I. Mahmudov
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Abstract:In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of the law and the state of the process. We establish a new version of the maximum principle for discrete-time stochastic optimal control problems. Moreover, the cost functional is also of the mean-field type. This maximum principle differs from the classical principle since we introduce new discrete-time backward (matrix) stochastic equations. Based on the discrete-time backward stochastic equations where the adjoint equations turn out to be discrete backward SDEs with mean field, we obtain necessary first-order and sufficient optimality conditions for the stochastic discrete optimal control problem. To verify, we apply the result to production and consumption choice optimization problem.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2210.01197 [math.OC]
  (or arXiv:2210.01197v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.01197

Submission history

From: Arzu Ahmadova [view email]
[v1] Mon, 3 Oct 2022 19:21:15 UTC (27 KB)
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