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

共 50 条

[1] Martingale Approach to Stochastic Control with Discretionary Stopping
Ioannis Karatzas
Ingrid-Mona Zamfirescu
[J]. Applied Mathematics and Optimization, 2006, 53 : 163 - 184
[2] Martingale approach to stochastic control with discretionary stopping
Karatzas, I
Zamfirescu, IM
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2006, 53 (02): : 163 - 184
[3] Optimal stopping and stochastic control differential games for jump diffusions
Baghery, Fouzia
Haadem, Sven
Oksendal, Bernt
Turpin, Isabelle
[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2013, 85 (01) : 85 - 97
[4] A Stochastic Control Approach for Constrained Stochastic Differential Games with Jumps and Regimes
Savku, Emel
[J]. MATHEMATICS, 2023, 11 (14)
[5] Stochastic games of control and stopping for a linear diffusion
Karatzas, Annis
Sudderth, William
[J]. RANDOM WALK, SEQUENTIAL ANALYSIS AND RELATED TOPICS: A FESTSCHRIFT IN HONOR OF YUAN-SHIH CHOW, 2006, : 100 - +
[6] Error estimates for stochastic differential games: the adverse stopping case
Bonnans, JF
Maroso, S
Zidani, H
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2006, 26 (01) : 188 - 212
[7] Zero-sum stochastic games with stopping and control
Ghosh, Mrinal K.
Rao, K. S. Mallikarjuna
[J]. OPERATIONS RESEARCH LETTERS, 2007, 35 (06) : 799 - 804
[8] Stochastic differential games: the potential approach
Fonseca-Morales, A.
Hernandez-Lerma, O.
[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2020, 92 (07) : 1125 - 1138
[9] Differential Games of Mixed Type with Control and Stopping Times
Ghosh, Mrinal K.
Rao, Mallikarjuna K. S.
Sheetal, Dharmatti
[J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2009, 16 (02): : 143 - 158
[10] Differential Games of Mixed Type with Control and Stopping Times
Mrinal K. Ghosh
Mallikarjuna K. S. Rao
Dharmatti Sheetal
[J]. Nonlinear Differential Equations and Applications NoDEA, 2009, 16 : 143 - 158

← 1 2 3 4 5 →