Statistics Seminars 2019
Martedì 12 marzo 2019 ore 16
Aula seminari, Dipartimento di Scienze Statistiche, I piano
"BSDEs driven by a general random measure and optimal control for piecewise deterministic Markov processes"
Dott.ssa Elena Bandini, Università degli Studi di Milano-Bicocca
Abstract: 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-local 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"
Tutti gli interessati sono invitati a partecipare
Alberto Lanconelli
Dipartimento di Scienze Statistiche "Paolo Fortunati"
Alma Mater Studiorum - Università di Bologna
