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We prove a stochastic representation formula for the viscosity solution ofDirichlet terminal-boundary value problem for a degenerateHamilton-Jacobi-Bellman integro-partial differential equation in a boundeddomain. We show that the unique viscosity solution is the value function of theassociated stochastic optimal control problem. We also obtain the dynamicprogramming principle for the associated stochastic optimal control problem ina bounded domain.

Stochastic Representations for Solutions to Parabolic Dirichlet Problems for Nonlocal Bellman Equations