@article{7478240f210848bf9908e2ea9fe6f4f7, title = "STOCHASTIC REPRESENTATIONS FOR SOLUTIONS TO PARABOLIC DIRICHLET PROBLEMS FOR NONLOCAL BELLMAN EQUATIONS", 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.", keywords = "Dynamic programming principle, Hamilton-Jacobi-Bellman equation, Integro-PDE, L{\'e}vy process, Stochastic representation formula, Value function, Viscosity solution, Dynamic programming principle, Hamilton-Jacobi-Bellman equation, Integro-PDE, L{\'e}vy process, Stochastic representation formula, Value function, Viscosity solution, Dynamic programming principle, Hamilton-Jacobi-Bellman equation, Integro-PDE, L{\'e}vy process, Stochastic representation formula, Value function, Viscosity solution", author = "Ruoting GONG and Chenchen MOU and Andrzej {\'S}WI{\c E}CH", year = "2019", month = dec, doi = "10.1214/19-AAP1473", language = "English", volume = "29", pages = "3271--3310", journal = "Annals of Applied Probability", issn = "1050-5164", publisher = "Institute of Mathematical Statistics", number = "6", }