10h30 Marco Fuhrman (Politecnico di Milano) Optimal control of pure jump Markov processes
and constrained backward stochastic differential equations
Résumé : We consider an optimal stochastic control problem for
general
pure jump Markov processes described by their rate transition
measure and
we derive a probabilistic representation for the value function
which is
a solution to the corresponding Hamilton-Jacobi-Bellman (HJB)
equation of
integral type. The method we use, introduced in recent papers by I. Kharroubi, H
Pham,
J. Ma, J. Zhang, R. Elie, is based on a randomization of the control process. For the
randomized
system we introduce a "dual" control problem whose value function can be
represented in terms of a constrained backward stochastic differential equations with
partially
nonpositive jumps. Finally we identify both value functions via analysis of the HJB
equation. This is a joint work with Elena Bandini (Politecnico di Milano).