Optimal Relaxed Control for a Decoupled G-FBSDE

Hafida Bouanani, Omar Kebiri (), Carsten Hartmann and Amel Redjil
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Hafida Bouanani: University of Saida Dr Moulay Tahar
Omar Kebiri: The Free University of Berlin
Carsten Hartmann: University of Cottbus
Amel Redjil: Badji-Mokhtar University

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 3, No 2, 1027-1059

Abstract: Abstract In this paper we study a system of decoupled forward-backward stochastic differential equations driven by a G-Brownian motion (G-FBSDEs) with non-degenerate diffusion. Our objective is to establish the existence of a relaxed optimal control for a non-smooth stochastic optimal control problem. The latter is given in terms of a decoupled G-FBSDE. The cost functional is the solution of the backward stochastic differential equation at the initial time. The key idea to establish existence of a relaxed optimal control is to replace the original control problem by a suitably regularised problem with mollified coefficients, prove the existence of a relaxed control, and then pass to the limit.

Keywords: Decoupled forward–backward stochastic differential equations; G-Brownian motion; Relaxed optimal control; Hamilton–Jacobi–Bellman equation; 60H05; 60H20; 60J75; 93E20; 91G80; 91B70 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02495-2

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