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Stochastic maximum principle for partially observed optimal control problem of McKean–Vlasov FBSDEs with Teugels martingales

  • Rafik Kaouache EMAIL logo , Imad Eddine Lakhdari ORCID logo and Youcef Djenaihi
Published/Copyright: June 20, 2024

Abstract

In this paper, we study the stochastic maximum principle for a partially observed optimal control problem of forward-backward stochastic differential equations (FBSDEs for short) of McKean–Vlasov type driven by both a family of Teugels martingales and an independent Brownian motion. The coefficients of the system and the cost functional depending on the state of the solution process as well as its probability law and the control variable. We establish partially observed necessary conditions of optimality for this system 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 application of the general theory, a partially observed linear-quadratic control problem of McKean–Vlasov type is studied in terms of stochastic filtering.

MSC 2020: 93E20; 60H10
  1. Communicated by: Vyacheslav L. Girko

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Received: 2023-04-26
Accepted: 2024-03-24
Published Online: 2024-06-20
Published in Print: 2024-09-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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