THE DIVIDEND PROBLEM WITH A FINITE HORIZON

• 成果类型: Article
• 署名作者: De Angelis, Tiziano; Ekstrom, Erik
• 署名单位: University of Leeds; Uppsala University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1286
• 发表日期: 2017
• 页码: 3525-3546
• 关键词: singular stochastic-control; optimal consumption problem; time-horizon; probabilistic aspects; follower problems; russian options; brownian model; connections; absorption; fuel

摘要

We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod reflection of the fund's value at a time-dependent optimal boundary. Our results are obtained by establishing for the first time a new connection between singular control problems with an absorbing boundary and optimal stopping problems on a diffusion reflected at 0 and created at a rate proportional to its local time.