Author(s)

Beatrice Gaviraghi¹, Andreas Schindele¹, Mario Annunziato², Alfio Borzì¹

¹Institut für Mathematik, Universität Würzburg, Würzburg, Germany.
²Dipartimento di Matematica, Università degli Studi di Salerno, Fisciano (SA), Italy.

A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.

Jump-Diffusion Processes, Partial Integro-Differential Fokker-Planck Equation, Optimal Control Theory, Nonsmooth Optimization, Proximal Methods

Gaviraghi, B. , Schindele, A. , Annunziato, M. and Borzì, A. (2016) On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes. Applied Mathematics, 7, 1978-2004. doi: 10.4236/am.2016.716162.