Martingale approach to stochastic differential games of control and stopping

• 成果类型: Article
• 署名作者: Karatzas, Ioannis; Zamfirescu, Ingrid-Mona
• 署名单位: Columbia University; City University of New York (CUNY) System; Baruch College (CUNY)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP367
• 发表日期: 2008
• 页码: 1495-1527
• 关键词: dynamic-programming conditions; MAXIMUM PRINCIPLE; EXISTENCE; EQUATIONS; time

摘要

We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate conditions, we show that the game has a value and construct a saddle pair of optimal control and stopping strategies. Crucial in this construction is a characterization of saddle pairs in terms of pathwise and martingale properties of suitable quantities.