Optimal impulsive control of piecewise deterministic Markov processes

In this paper, we study the infinite-horizon expected discounted continuous-time optimal control problem for Piecewise Deterministic Markov Processes with both impulsive and gradual (also called continuous) controls. The set of admissible control strategies is supposed to be formed by policies possi...

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Bibliographic Details
Published in:Stochastics (Abingdon, Eng. : 2005) Vol. 88; no. 7; pp. 1073 - 1098
Main Authors: Dufour, F., Horiguchi, M., Piunovskiy, A. B.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.10.2016
Taylor & Francis Ltd
Taylor & Francis: STM, Behavioural Science and Public Health Titles
Subjects:
discounted cost
Economic models
impulsive control
Insurance claims
Markov analysis
Markov processes
Mathematical analysis
Mathematics
Optimal control
Optimization
Optimization and Control
piecewise deterministic Markov process
Policies
Primary: 90C40
Probability theory
Production planning
Randomness
Secondary: 60J25
Strategy
Discounted cost
Impulsive control
Piecewise deterministic Markov process
Optimal control
ISSN:1744-2508, 1744-2516
Online Access:Get full text
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Summary:In this paper, we study the infinite-horizon expected discounted continuous-time optimal control problem for Piecewise Deterministic Markov Processes with both impulsive and gradual (also called continuous) controls. The set of admissible control strategies is supposed to be formed by policies possibly randomized and depending on the past-history of the process. We assume that the gradual control acts on the jump intensity and on the transition measure, but not on the flow. The so-called Hamilton-Jacobi-Bellman (HJB) equation associated to this optimization problem is analyzed. We provide sufficient conditions for the existence of a solution to the HJB equation and show that the solution is in fact unique and coincides with the value function of the control problem. Moreover, the existence of an optimal control strategy is proven having the property to be stationary and non-randomized.
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ISSN:1744-2508
1744-2516
DOI:10.1080/17442508.2016.1197925