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- W1552220249 abstract "In the present work, we employ backward stochastic differential equations (BSDEs) to study the optimal control problem of semi-Markov processes on a finite horizon, with general state and action spaces. More precisely, we prove that the value function and the optimal control law can be represented by means of the solution of a class of BSDEs driven by a semi-Markov process or, equivalently, by the associated random measure. We also introduce a suitable Hamilton–Jacobi–Bellman (HJB) equation. With respect to the pure jump Markov framework, the HJB equation in the semi-Markov case is characterized by an additional differential term $$partial _a$$ . Taking into account the particular structure of semi-Markov processes, we rewrite the HJB equation in a suitable integral form which involves a directional derivative operator D related to $$partial _a$$ . Then, using a formula of It $$hat{text{ o }}$$ type tailor-made for semi-Markov processes and the operator D, we are able to prove that a BSDE of the above-mentioned type provides the unique classical solution to the HJB equation, which identifies the value function of our control problem." @default.
- W1552220249 created "2016-06-24" @default.
- W1552220249 creator A5011090496 @default.
- W1552220249 creator A5063463468 @default.
- W1552220249 date "2016-12-19" @default.
- W1552220249 modified "2023-10-01" @default.
- W1552220249 title "Optimal control of semi-Markov processes with a backward stochastic differential equations approach" @default.
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- W1552220249 doi "https://doi.org/10.1007/s00498-016-0181-6" @default.
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