A Stochastic Maximum Principle for Partially Observed Optimal Control Problem of Mckean-Vlasov FBSDEs with Random Jumps

被引:2
作者
Abba, Khedidja [1 ]
Lakhdari, Imad Eddine [1 ]
机构
[1] Biskra Univ, Lab Math Anal Probabil & Optimizat, POB 145, Biskra 07000, Algeria
关键词
Stochastic maximum principle; Forward-backward stochastic differential equations with jump processes; Partially observed optimal control; McKean-Vlasov differential equations; Derivative with respect to probability measures; DIFFERENTIAL-EQUATIONS; SYSTEMS;
D O I
10.1007/s41980-023-00803-6
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we study the stochastic maximum principle for partially observed optimal control problem of forward-backward stochastic differential equations of McKean-Vlasov type driven by a Poisson random measure and an independent Brownian motion. The coefficients of the system and the cost functional depend on the state of the solution process as well as of its probability law and the control variable. Necessary and sufficient conditions of optimality for this systems are established under assumption that the control domain is supposed to be convex. Our main result is based on Girsavov's theorem and the derivatives with respect to probability law. As an illustration, a partially observed linear-quadratic control problem of McKean-Vlasov forward-backward stochastic differential equations type is studied in terms of the stochastic filtering.
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页数:30
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