Publication: Maximum principle for partially observed risk-sensitive optimal control problem of McKean?Vlasov FBSDEs involving impulse controls
Date
2024
Authors
Lakhdari I.E.
Djenaihi Y.
Kaouache R.
Boulaaras S.
Jan R.
Journal Title
Journal ISSN
Volume Title
Publisher
Birkhauser
Abstract
In this research, we investigate the maximum principle pertaining to risk-sensitive optimal control problems under partial observation, modeled by forward?backward stochastic differential equations (FBSDEs) of the general regularity McKean?Vlasov form. An important aspect of these equations is that their coefficients are nonlinearly influenced by both the state process and its distribution. The control variable consists of two components: a continuous control and an impulse control. The cost functional is an exponential of integral type based on the regularity McKean?Vlasov framework. By applying Girsanov?s theorem and taking derivatives with respect to the probability distribution, we establish the risk-sensitive maximum principle. This principle is formulated using variational inequalities, under the assumption that the control domain is convex. Moreover, the sufficient conditions of optimality is obtained under certain concavity assumptions. As an application, the main outcomes are used to solve a linear-quadratic risk-sensitive optimal control problem of the regularity McKean?Vlasov type, both under partial and full observation conditions. ? The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.