Linear Quadratic Control Problems for Mean Field Stochastic Differential Equation with Jumps: Application in Exhaustible Resources Production

Anis Matoussi (1) , Mohamed Mnif (2) , Chefia Ziri (1)

1 LMM - Laboratoire Manceau de Mathématiques
2 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]

In this paper, we are interested by a stochastic model of production of an exhaustible resource, such as oil. It is known that such reserves are depleted resources, but there is a possibility of exploration and discovery of new reserves which ensure the accumulating or the upkeep of this reserves' level. We modelled the new discoveries by a jump process with intensity given by the exploration effort. We employed a weak formulation of the standard martingale optimality principle to solve a linear quadratic stochastic control problem for mean field stochastic differential equation with jumps in both cases: finite and infinite horizon.

Mots clés: Linear quadratic optimal control; Mean field SDEs with jumps; Mean field BSDEs with jumps; Riccati equation; Exhaustible resources; Stochastic control; Jumps diffusion process

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

Anis Matoussi, Mohamed Mnif, Chefia Ziri. Linear Quadratic Control Problems for Mean Field Stochastic Differential Equation with Jumps: Application in Exhaustible Resources Production. 2022. ⟨hal-03815082⟩