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

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATICAL METHODS OF OPERATIONS RESEARCH; v. 93, n. 2 JAN 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 14/50851-0 - INCT 2014: Instituto Nacional de Ciência e Tecnologia para Sistemas Autônomos Cooperativos Aplicados em Segurança e Meio Ambiente
• Beneficiário: Marco Henrique Terra
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 14/50279-4 - Brasil Research Centre for Gas Innovation
• Beneficiário: Julio Romano Meneghini
• Linha de fomento: Auxílio à Pesquisa - Programa Centros de Pesquisa em Engenharia