Optimal control of stochastic delayed systems with jumps

Delphine David (1)

1 MIA - Mathématiques, Image et Applications - EA 3165

We consider the optimal control of stochastic delayed systems with jumps, in which both the state and controls can depend on the past history of the system, for a value function which depends on the initial path of the process. We derive the Hamilton-Jacobi-Bellman equation and the associated verification theorem and prove a necessary and a sufficient maximum principles for such problems. Explicit solutions are obtained for a mean-variance portfolio problem and for the optimal consumption and portfolio case in presence of a financial market with delay and jumps.

Mots clés: Stochastic delayed systems with jumps; Hamilton-Jacobi-Bellman equation; Pontryagin-type maximum principle; sufficient maximum principle.; sufficient maximum principle

Domaines: Optimisation et contrôle [math.OC]

Delphine David. Optimal control of stochastic delayed systems with jumps. 2008. ⟨hal-00373642⟩