Infinite Horizon Stochastic Impulse Control with Delay and Random Coefficients

• 成果类型: Article
• 署名作者: Djehiche, Boualem; Hamadene, Said; Hdhiri, Ibtissem; Zaatra, Helmi
• 署名单位: Royal Institute of Technology; Le Mans Universite; Universite de Gabes
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1145
• 发表日期: 2022
• 页码: 665-689
• 关键词: finite-horizon

摘要

We study a class of infinite horizon impulse control problems with execution delay when the dynamics of the system is described by a general stochastic process adapted to the Brownian filtration. The problem is solved by means of probabilistic tools relying on the notion of Snell envelope and infinite horizon reflected backward stochastic differential equations. This allows us to establish the existence of an optimal strategy over all admissible strategies.