Utility Maximization Problem with Uncertainty and a Jump Setting

Sarah Kaakai (1) , Anis Matoussi (1) , Achraf Tamtalini (1)

1 LMM - Laboratoire Manceau de Mathématiques

We study a robust utility maximization problem in the unbounded case with a general penalty term and information including jumps. We focus on time consistent penalties and we prove that there exists an optimal probability measure solution of the robust problem. Then, we characterize the dynamic value process of our stochastic control problem as the unique solution of a Quadratic-Exponential BSDE.

Mots clés: Utility maximization; Robustness; Quadratic BSDEs with jumps; Time-consistent penalties; Bellman Martingale Optimality principle; Uncertainty; Stochastic control

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]

Sarah Kaakai, Anis Matoussi, Achraf Tamtalini. Utility Maximization Problem with Uncertainty and a Jump Setting. 2022. ⟨hal-03813812v3⟩