Forward-backward doubly stochastic differential equations with random jumps and related games

被引：5

作者：

Zhu, Qingfeng ^{[1
,2
,3
,4
]}

Shi, Yufeng ^{[3
,4
,5
]}

Teng, Bin ^{[3
,4
]}

机构：

[1] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan, Peoples R China

[2] Shandong Univ Finance & Econ, Shandong Key Lab Blockchain Finance, Jinan, Peoples R China

[3] Shandong Univ, Inst Financial Studies, Jinan 250100, Peoples R China

[4] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

[5] Shandong Univ Finance & Econ, Sch Stat, Jinan, Peoples R China

来源：

ASIAN JOURNAL OF CONTROL | 2021年 / 23卷 / 02期

基金：

国家重点研发计划; 中国国家自然科学基金;

关键词：

forward-backward doubly stochastic differential equations; LQ nonzero sum differential games; random measure; Poisson process; MAXIMUM PRINCIPLE; CONTROL SYSTEMS; TIME-REVERSAL; DRIVEN; PDIES;

D O I：

10.1002/asjc.2344

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A type of forward-backward doubly stochastic differential equations driven by Brownian motions and the Poisson process (FBDSDEP) is studied. Under some monotonicity assumptions, the existence and uniqueness results for measurable solutions of FBDSDEP are established via a method of continuation. Then the continuity and differentiability of the solutions to FBDSDEP depending on parameters is discussed. Furthermore, these results were applied to backward doubly stochastic linear quadratic (LQ) nonzero sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the FBDSDEP.

引用

页码：962 / 978

页数：17

共 41 条

[1]

Applebaum D., 2009, Levy Process and Stochastic Calculus

[2] Backward doubly SDEs and SPDEs with superlinear growth generators [J].

Bahlali, Khaled ;

Gatt, Rafika ;

Mansouri, Badreddine ;

Mtiraoui, Ahmed .

STOCHASTICS AND DYNAMICS, 2017, 17 (01)

[3] Optimality conditions of controlled backward doubly stochastic differential equations [J].

Bahlali, Seid ;

Gherbal, Boulakhras .

RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2010, 18 (03) :247-265

[4] Weak solutions for SPDEs and Backward Doubly Stochastic Differential Equations [J].

Bally, V ;

Matoussi, A .

JOURNAL OF THEORETICAL PROBABILITY, 2001, 14 (01) :125-164

[5]

Da Prato G, 1998, STOCH ANAL APPL, V16, P993

[6] Some results of backward Ito formula [J].

Da Prato, Giuseppe ;

Menaldi, Jose-Luis ;

Tubaro, Luciano .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2007, 25 (03) :679-703

[7] Backward stochastic differential equations in finance [J].

El Karoui, N ;

Peng, S ;

Quenez, MC .

MATHEMATICAL FINANCE, 1997, 7 (01) :1-71

[8] Nonzero sum linear-quadratic stochastic differential games and backward-forward equations [J].

Hamadène, S .

STOCHASTIC ANALYSIS AND APPLICATIONS, 1999, 17 (01) :117-130

[9] MAXIMUM PRINCIPLE FOR BACKWARD DOUBLY STOCHASTIC CONTROL SYSTEMS WITH APPLICATIONS [J].

Han, Yuecai ;

Peng, Shige ;

Wu, Zhen .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2010, 48 (07) :4224-4241

[10] TIME-REVERSAL OF DIFFUSIONS [J].

HAUSSMANN, UG ;

PARDOUX, E .

ANNALS OF PROBABILITY, 1986, 14 (04) :1188-1205

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