RISK-SENSITIVE CONTROL FOR A CLASS OF DIFFUSIONS WITH JUMPS

• 成果类型: Article
• 署名作者: Arapostathis, Ari; Biswas, Anup
• 署名单位: University of Texas System; University of Texas Austin; Indian Institute of Science Education & Research (IISER) Pune
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1758
• 发表日期: 2022
• 页码: 4106-4142
• 关键词: time markov-processes; ergodic control; Bellman equations; asymptotic evaluation; process expectations; probabilities; CONVERGENCE; EIGENVALUE; EXISTENCE

摘要

We consider a class of diffusions controlled through the drift and jump size, and driven by a jump Levy process and a nondegenerate Wiener pro-cess, and we study infinite horizon (ergodic) risk-sensitive control problems for this model. We start with the controlled Dirichlet eigenvalue problem in smooth bounded domains, which also allows us to generalize current results in the literature on exit rate control problems. Then we consider the infi-nite horizon average risk-sensitive minimization and maximization problems on the whole domain. Under suitable hypotheses, we establish existence and uniqueness of a principal eigenfunction for the Hamilton-Jacobi-Bellman (HJB) operator on the whole space, and fully characterize stationary Markov optimal controls as the measurable selectors of this HJB equation.