Characterization of optimality for controlled jump diffusion processes

  • Farid Chighoub


This paper studies necessary as well as su¢ cient conditions of optimality for a general class of controlled diffusions with Jumps. More precisely, The state of the system is described by a nonlinear stochastic differential equation, driven by a Poisson random measure and an independent Brownian motion.
A discussion on veriÂ…cation results is performed, by using recent results on the relationship between the adjoint processes and the value function, in the language of viscosity solutions and the associated super-differentials. In a second step, we prove the nonsmooth version of the necessity part of the veriÂ…cation theorem in terms of sub-differential, rather than derivatives of the value function.