Optimal stopping of linear diffusions with random discounting

• 成果类型: Article
• 署名作者: Dayanik, Savas
• 署名单位: Princeton University; Princeton University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1070.0308
• 发表日期: 2008
• 页码: 645-661
• 关键词: singular stochastic-control; connections

摘要

We propose a new solution method for optimal stopping problems with random discounting for linear diffusions whose state space has a combination of natural, absorbing, or reflecting boundaries. The method uses a concave characterization of excessive functions for linear diffusions killed at a rate determined by a Markov additive functional and reduces the original problem to an undiscounted optimal stopping problem for a standard Brownian motion. The latter can be solved essentially by inspection. The necessary and sufficient conditions for the existence of an optimal stopping rule are proved when the reward function is continuous. The results are illustrated on examples.