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 HamiltonâJacobiâBellman (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 âa. 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 âa. Then, using a formula of Ito^ 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
Bandini, E., & Confortola, F. (2017). Optimal control of semi-Markov processes with a backward stochastic differential equations approach. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 29(1) [10.1007/s00498-016-0181-6].
Citazione: | Bandini, E., & Confortola, F. (2017). Optimal control of semi-Markov processes with a backward stochastic differential equations approach. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 29(1) [10.1007/s00498-016-0181-6]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Presenza di un coautore afferente ad Istituzioni straniere: | No | |
Titolo: | Optimal control of semi-Markov processes with a backward stochastic differential equations approach | |
Autori: | Bandini, E; Confortola, F | |
Autori: | CONFORTOLA, FULVIA (Corresponding) | |
Data di pubblicazione: | 2017 | |
Lingua: | English | |
Rivista: | MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00498-016-0181-6 | |
Appare nelle tipologie: | 01 - Articolo su rivista |
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