Risk-sensitive discounted cost criterion for continuous-time Markov decision processes on a general state space

Subrata Golui () and Chandan Pal ()
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Subrata Golui: Indian Institute of Technology Guwahati
Chandan Pal: Indian Institute of Technology Guwahati

Mathematical Methods of Operations Research, 2022, vol. 95, issue 2, No 3, 219-247

Abstract: Abstract In this paper, we consider risk-sensitive discounted control problem for continuous-time jump Markov processes taking values in general state space. The transition rates of underlying continuous-time jump Markov processes and the cost rates are allowed to be unbounded. Under certain Lyapunov condition, we establish the existence and uniqueness of the solution to the Hamilton–Jacobi–Bellman equation. Also, we prove the existence of optimal risk-sensitive control in the class of Markov control and completely characterized the optimal control.

Keywords: Continuous-time Markov decision process; History-dependent control; General state space; Risk-sensitive discounted criterion; HJB equation; Optimal control (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00186-022-00779-9

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