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Seminario: Optimal control of non-diffusive stochastic processes: constrained BSDE representation of the value function

Mercoledì 21 Ottobre 2015, ore 14:30 - Sala Riunioni VII piano - Elena Bandini

ARGOMENTI: Seminari

Mercoledì 21 Ottobre 2015 alle ore 14:30 in Sala Riunioni VII piano, Elena Bandini terrà un seminario dal titolo "Optimal control of non-diffusive stochastic processes: constrained BSDE representation of the value function".

Abstract
We consider classical finite and infinite horizon optimal control problems for continuous-time jump Markov processes described by means of their controlled local characteristics. For this class of problems the value function can often be described as the unique solution to the corresponding Hamilton-Jacobi-Bellman equation. We prove a probabilistic representation for the value function, known as nonlinear Feynman-Kac formula. It relates the value function with a backward stochastic differential equation (BSDE) driven by a random measure and with a sign constraint on its martingale part. We also prove existence and uniqueness results for this class of constrained BSDEs. The connection of the control problem with the constrained BSDE uses a control randomization method recently developed in the works of I. Kharroubi and H. Pham and their co-authors in a diffusive framework. This approach also allows to prove that the value function of the original non-dominated control problem coincides with the value function of an auxiliary dominated control problem, expressed in terms of equivalent changes of probability measures.

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