Approximations for Functionals and Optimal Control Problems on Jump Diffusion Processes.

摘要

The paper treats approximations to stochastic differential equations with both a diffusion and a jump component, and to associated functionals and partial-differential-integral equations of the (degenerate or not) elliptic or parabolic type. Approximations for the optimal control problem on such a model, or for the associated non-linear partial-differential-integral equation, are discussed. The techniques are purely probabilistic and are extensions of those in another paper by the first author, which dealt with the diffusion case.