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On stochastic maximum principle for risk-sensitive of fully coupled forward-backward stochastic control of mean-field type with application

  • * Corresponding author: Adel Chala

    * Corresponding author: Adel Chala 

The first author is supported by PRFU project N: C00L03UN070120180002

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  • In this paper, we are concerned with an optimal control problem where the system is driven by fully coupled forward-backward stochastic differential equation of mean-field type with risk-sensitive performance functional. We study the risk-neutral model for which an optimal solution exists as a preliminary step. This is an extension of the initial stochastic control problem in this type of risk-sensitive performance problem, where an admissible set of controls are convex. We establish necessary as well as sufficient optimality conditions for the risk-sensitive performance functional control problem. Finally, we illustrate our main result of this paper by giving two examples of risk-sensitive control problem under linear stochastic dynamics with exponential quadratic cost function, the second example will be a mean-variance portfolio with a recursive utility functional optimization problem involving optimal control. The explicit expression of the optimal portfolio selection strategy is obtained in the state feedback.

    Mathematics Subject Classification: Primary: 93E20, 60H30; Secondary: 60H10, 91B28.

    Citation:

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