A non-zero sum differential game of mean-field backward stochastic differential equation

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.

show abstract

“…investment strategies are obtained. The results obtained here extend the first two authors' previous works of [12,14], and [28].…”

Section: Introducesupporting

confidence: 91%

“…Putting (28) into the second equation of (23), and comparing the coefficients of (29) and (23), we get…”

Section: Symmetric Informationmentioning

confidence: 99%

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

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…With the help of the initial value and terminal value of Q(·) and p(·), respectively, in the equation (3.9), and the condition h 1yy (y) ≡h 1 , we have 16) and…”

Section: Optimization For the Leadermentioning

confidence: 99%

“…Huang et al [15] studied a backward mean-field linear-quadratic-Gaussian games of weakly coupled stochastic large-population system, and two classes of foregoing games are discussed and their decentralized strategies are derived through the consistency condition. Huang and Wang [16] discussed a kind of non-zero sum differential game of mean-field BSDE. Wang et al [38] studied a kind of LQ non-zero sum differential game driven by BSDE with asymmetric information.…”

Section: Introductionmentioning

confidence: 99%

A Stackelberg Game of Backward Stochastic Differential Equations with Applications

Zheng

Shi

2019

Dyn Games Appl

View full text Add to dashboard Cite

This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs) with partial information, where the information of the follower is a sub-σ-algebra of that of the leader. Necessary and sufficient conditions of the optimality for the follower and the leader are first given for the general problem, by the partial information stochastic maximum principles of BSDEs and forward-backward stochastic differential equations (FBSDEs), respectively. Then a linear-quadratic (LQ) Stackelberg game of BSDEs with partial information is investigated. The state estimate feedback representation for the optimal control of the follower is first given via two Riccati equations. Then the leader's problem is formulated as an optimal control problem of FBSDE. Four high-dimensional Riccati equations are introduced to represent the state estimate feedback for the optimal control of the leader. Theoretic results are applied to a pension fund management problem of two players in the financial market.

show abstract

“…Huang et al [15] studied a backward mean-field linear-quadratic-Gaussian games of weakly coupled stochastic large-population system, and two classes of foregoing games are discussed and their decentralized strategies are derived through the consistency condition. Huang and Wang [16] discussed a kind of non-zero sum differential game of mean-field BSDE. Wang et al [39] studied a kind of LQ non-zero sum differential game driven by BSDE with asymmetric information.…”

mentioning

confidence: 99%

A stackelberg game of backward stochastic differential equations with partial information

Zheng¹,

Shi²

2021

MCRF

View full text Add to dashboard Cite

<p style='text-indent:20px;'>This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs) with partial information, where the information of the follower is a sub-<inline-formula><tex-math id="M1">\begin{document}$ \sigma $\end{document}</tex-math></inline-formula>-algebra of that of the leader. Necessary and sufficient conditions of the optimality for the follower and the leader are first given for the general problem, by the partial information stochastic maximum principles of BSDEs and forward-backward stochastic differential equations (FBSDEs), respectively. Then a linear-quadratic (LQ) Stackelberg game of BSDEs with partial information is investigated. The state estimate feedback representation for the optimal control of the follower is first given via two Riccati equations. Then the leader's problem is formulated as an optimal control problem of FBSDE. Four high-dimensional Riccati equations are introduced to represent the state estimate feedback for the optimal control of the leader. Theoretic results are applied to a pension fund management problem of two players in the financial market.</p>

show abstract

A non-zero sum differential game of mean-field backward stochastic differential equation

Cited by 4 publications

References 10 publications

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

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

A Stackelberg Game of Backward Stochastic Differential Equations with Applications

A stackelberg game of backward stochastic differential equations with partial information

Contact Info

Product

Resources

About