Stochastic representations for solutions to parabolic Dirichlet problems for nonlocal Bellman equations

Authors
Gong Ruoting Mou Chenchen .wi.ch Andrzej
Citation
Gong Ruoting et al., Stochastic representations for solutions to parabolic Dirichlet problems for nonlocal Bellman equations, Annals of applied probability , 29(6), 2019, pp. 3271-3310
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
29
Issue
6
Year of publication
2019
Pages
3271 - 3310
Database
ACNP
SICI code
Abstract
We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton.Jacobi.Bellman integro-partial differential equation in a bounded domain. We show that the unique viscosity solution is the value function of the associated stochastic optimal control problem. We also obtain the dynamic programming principle for the associated stochastic optimal control problem in a bounded domain.