A kind of LQ non-zero sum differential game of backward stochastic differential equation with asymmetric information

Wang, Guangchen; Xiao, Hua; Xiong, Jie

doi:10.1016/j.automatica.2018.08.019

Cited by 48 publications

(30 citation statements)

References 19 publications

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“…Note that some Stackelberg differential games with partially observable information can be put into the above LQ model by the Girsanov transformation. See, for example, Shi et al [20], Wang et al [24].…”

Section: Problem Formulationmentioning

confidence: 99%

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Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information

2020

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This paper is concerned with the stochastic linear quadratic Stackelberg differential game with overlapping information, where the diffusion terms contain the control and state variables. Here the term "overlapping" means that there are common part between the follower's and the leader's information, while they have no inclusion relation. Optimal controls of the follower and the leader are obtained by the stochastic maximum principle, the direct calculation of the derivative of the cost functional and stochastic filtering. A new system of Riccati equations is introduced to represent the state estimate feedback of the Stackelberg equilibrium strategy. A special solvable case is then studied and is applied to the continuous-time principal-agent problem.

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Section: Problem Formulationmentioning

confidence: 99%

“…al. [24] focused on an LQ non-zero sum differential game problem derived by the BSDE with asymmetric information. Three classes of observable filtrations are described to classify the information available to the two players.…”

Section: Literature Review and The Contribution Of This Papermentioning

confidence: 99%

Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information

2020

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“…Since (13) and (14) are coupled with each other, it is difficult to prove their existence and uniqueness except for some special cases. For example, Hypothesis 6 C 2 (t) = -C 2 (t).…”

Section: Symmetric Informationmentioning

confidence: 99%

“…Wang and Yu [12] established a necessary condition and a verification theorem for open-loop Nash equilibrium point of non-zero sum differential game of BSDE under partial information. Furthermore, Wang et al [13] discussed asymmetric information LQ non-zero sum differential game of BSDE and gave the feedback Nash equilibrium points. See also Wang and Yu [14], Li and Yu [15] for more information.…”

Section: Introductionmentioning

confidence: 99%

An asymmetric information non-zero sum differential game of mean-field backward stochastic differential equation with applications

2019

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This paper is concerned with a kind of non-zero sum differential game driven by mean-field backward stochastic differential equation (MF-BSDE) with asymmetric information, whose novel feature is that both the state equation and the cost functional are of mean-field type. A necessary condition and a sufficient condition for Nash equilibrium point of the above problem are established. As applications, a mean-field linear-quadratic (MF-LQ) problem and a financial problem are studied.

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“…In addition, Shi and Wang [8] studied a non-zero sum stochastic differential game of BSDE with time-delayed generator. Wang et al [9] discussed asymmetric information linear-quadratic (LQ) non-zero sum differential game of BSDE, and gave the feedback Nash equilibrium points. About other applications of BSDE, please refer to Zhang [10], Li et al [11], El Karoui et al [12], and Yong and Zhou [13] for more information.…”

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confidence: 99%

A kind of non-zero sum mixed differential game of backward stochastic differential equation

Zhang

2020

Adv Differ Equ

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This paper is concerned with a non-zero sum mixed differential game problem described by a backward stochastic differential equation. Here the term "mixed" means that this game problem contains a deterministic control v 1 of Player 1 and a random control process v 2 of Player 2. By virtue of the classical variational method, a necessary condition and an Arrow's sufficient condition for the mixed stochastic differential game problem are presented. A linear-quadratic mixed differential game problem is discussed, and the corresponding Nash equilibrium point is explicitly expressed by the solution of mean-field forward-backward stochastic differential equation. The most distinguishing feature, compared with the existing literature, is that the optimal state process of the linear-quadratic game satisfies a linear mean-field backward stochastic differential equation. Finally, a home mortgage and wealth management problem is given to illustrate our theoretical results.

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A kind of LQ non-zero sum differential game of backward stochastic differential equation with asymmetric information

Cited by 48 publications

References 19 publications

Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information

Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information

An asymmetric information non-zero sum differential game of mean-field backward stochastic differential equation with applications

A kind of non-zero sum mixed differential game of backward stochastic differential equation

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