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• W2267376484 abstract "We consider a classical finite horizon optimal control problem for continuous-time pure jump Markov processes described by means of a rate transition measure depending on a control parameter and controlled by a feedback law. For this class of problems the value function can often be described as the unique solution to the corresponding Hamilton–Jacobi-Bellman equation. We prove a probabilistic representation for the value function, known as nonlinear Feynman–Kac formula. It relates the value function with a backward stochastic differential equation (BSDE) driven by a random measure and with a sign constraint on its martingale part. We also prove existence and uniqueness results for this class of constrained BSDEs. The connection of the control problem with the constrained BSDE uses a control randomization method recently developed by several authors. This approach also allows to prove that the value function of the original non-dominated control problem coincides with the value function of an auxiliary dominated control problem, expressed in terms of equivalent changes of probability measures." @default.
• W2267376484 created "2016-06-24" @default.
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• W2267376484 date "2017-05-01" @default.
• W2267376484 modified "2023-10-16" @default.
• W2267376484 title "Constrained BSDEs representation of the value function in optimal control of pure jump Markov processes" @default.
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• W2267376484 doi "https://doi.org/10.1016/j.spa.2016.08.005" @default.
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