Integro-differential optimality equations for the risk-sensitive control of piecewise deterministic Markov processes

Author(s)

Costa, O. L. V. ^[1] ; Dufour, F. ^[2]

Affiliation

^[1] Univ Sao Paulo, Escola Politecn, Dept Engn Telecomunicacoes & Controle, BR-05508010 Sao Paulo - Brazil

^[2] Univ Bordeaux, Inst Math Bordeaux, Inst Polytech Bordeaux, INRIA Bordeaux Sud Ouest, Team CQFD, IMB, Bordeaux - France

• Document type: Journal article
• Source: MATHEMATICAL METHODS OF OPERATIONS RESEARCH; v. 93, n. 2 JAN 2021.
• Web of Science Citations: 0

Abstract

In this paper we study the minimization problem of the infinite-horizon expected exponential utility total cost for continuous-time piecewise deterministic Markov processes with the control acting continuously on the jump intensity lambda and on the transition measure Q of the process. The action space is supposed to depend on the state variable and the state space is considered to have a frontier such that the process jumps whenever it touches this boundary. We characterize the optimal value function as the minimal solution of an integro-differential optimality equation satisfying some boundary conditions, as well as the existence of a deterministic stationary optimal policy. These results are obtained by using the so-called policy iteration algorithm, under some continuity and compactness assumptions on the parameters of the problem, as well as some non-explosive conditions for the process. (AU)

• FAPESP's process: 14/50851-0 - INCT 2014: National Institute of Science and Technology for Cooperative Autonomous Systems Applied in Security and Environment
• Grantee: Marco Henrique Terra
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 14/50279-4 - Brasil Research Centre for Gas Innovation
• Grantee: Julio Romano Meneghini
• Support Opportunities: Research Grants - Research Centers in Engineering Program