Statistics seminar 2019 - “BSDEs driven by a general random measure and optimal control for piecewise deterministic Markov processes”

  • Data: 12 marzo 2019 dalle 10:00 alle 12:00

  • Luogo: Dipartimento di Scienze Statistiche - via delle Belle Arti 41 - Aula II - piano terra

Elena Bandini - Università degli Studi di Milano-Bicocca

We consider an optimal control problem for piecewise deterministic Markov processes (PDMP) on a bounded state space. Here a pair of controls acts continuously on the deterministic flow and on the transition measure describing the jump dynamics of the process. For this class of control problems, the value function can be characterized as the unique viscosity solution to the corresponding integro-differential Hamilton-Jacobi-Bellman equation with a non-loca type boundary condition. We are able to provide a probabilistic representation for the value function in terms of a suitable backward stochastic differential equation, known as nonlinear Feynman-Kac formula. The jump mechanism from the boundary entails the presence of predictable jumps in the PDMP dynamics, so that the associated BSDE turns out to be driven by a random measure with predictable jumps. Existence and uniqueness results for such a class of equations are non-trivial and are related to recent works on well-posedness for BSDEs driven by non quasi-left-continuous random measures.

Alberto Lanconelli

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