Martingale approach to stochastic differential games of control and stopping

被引：40

作者：

Karatzas, Ioannis ^{[1
]}

Zamfirescu, Ingrid-Mona ^{[2
]}

机构：

[1] Columbia Univ, Dept Math, New York, NY 10027 USA

[2] CUNY Bernard M Baruch Coll, Dept Math, New York, NY 10010 USA

来源：

ANNALS OF PROBABILITY | 2008年 / 36卷 / 04期

关键词：

stochastic games; control; optimal stopping; martingales; Doob-Meyer decompositions; stochastic maximum principle; thrifty control strategies;

D O I：

10.1214/07-AOP367

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1495 / 1527

页数：33

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