Optimal control of direction of reflection for jump diffusions

Than Nam Vu (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We extend the optimal control of direction of reflection problem introduced in Bouchard [4] to the jump diffusion case. In a Brownian diffusion framework with jumps, the controlled process is defined as the solution of a stochastic differential equation (SDE) reflected at the boundary of a domain along oblique directions of reflection which are controlled by a predictable process which may have jumps. We also provide a version of the weak dynamic programming principle of Bouchard and Touzi [5] adapted to our context and which is sufficient to provide a viscosity characterization of the associated value function without requiring the usual heavy measurable selection arguments nor the a-priori continuity of the value function.

Mots clés: Optimal control; Dynamic programming; Skorokhod problem; Discontinuous viscosity solutions.; Discontinuous viscosity solutions

Domaines: Optimisation et contrôle [math.OC]

Than Nam Vu. Optimal control of direction of reflection for jump diffusions. 2011. ⟨hal-00562296⟩