Explicit theta-Schemes for Mean-Field Backward Stochastic Differential Equations

Sun, Yabing; Zhao, Weidong; Zhou, Tao

doi:10.1137/17m1161944

Cited by 16 publications

(10 citation statements)

References 18 publications

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“…In the fields about numerical algorithms and simulations for BSDEs, Peng and Xu [20] studied the convergence results of an explicit scheme based on approximating Brownian motion by random walk, which is efficient in programming, and they developed a software package based on this algorithm for BSDEs. Recently, the authors Sun, Zhao, and Zhou [22] proposed an explicit θ -scheme for MF-BSDEs, and we can get more results about MF-FBSDE simulations and numerical methods from other literature works of them.…”

Section: Follower Agent's Perturbationmentioning

confidence: 99%

Backward-forward linear-quadratic mean-field Stackelberg games

2021

Adv Differ Equ

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This paper studies a controlled backward-forward linear-quadratic-Gaussian (LQG) large population system in Stackelberg games. The leader agent is of backward state and follower agents are of forward state. The leader agent is dominating as its state enters those of follower agents. On the other hand, the state-average of all follower agents affects the cost functional of the leader agent. In reality, the leader and the followers may represent two typical types of participants involved in market price formation: the supplier and producers. This differs from standard MFG literature and is mainly due to the Stackelberg structure here. By variational analysis, the consistency condition system can be represented by some fully-coupled backward-forward stochastic differential equations (BFSDEs) with high dimensional block structure in an open-loop sense. Next, we discuss the well-posedness of such a BFSDE system by virtue of the contraction mapping method. Consequently, we obtain the decentralized strategies for the leader and follower agents which are proved to satisfy the ε-Nash equilibrium property.

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Section: Follower Agent's Perturbationmentioning

confidence: 99%

Backward-forward linear-quadratic mean-field Stackelberg games

2021

Adv Differ Equ

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“…Then by using the solutions of BSDEs, Peng [24] gave a probabilistic interpretation for quasilinear parabolic partial differential equations (PDEs). Since then, the study on FBSDEs has been extensively conducted due to its applications in research on PDEs [6,17,24], mathematical finance [11,15,20], stochastic optimal control [14,23], and mean-field BSDEs [2,3,26,28], to name a few. However, the analytic solutions of FBSDEs are seldom known.…”

Section: Introductionmentioning

confidence: 99%

Explicit High Order One-Step Methods for Decoupled Forward Backward Stochastic Differential Equations

sci¹

2021

AAMM

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By using the Feynman-Kac formula and combining with It ô-Taylor expansion and finite difference approximation, we first develop an explicit third order onestep method for solving decoupled forward backward stochastic differential equations. Then based on the third order one, an explicit fourth order method is further proposed. Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.

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“…After that Peng and Wu proved the existence and uniqueness of the solution of fully coupled FBSDEs with an arbitrarily large time duration in [19]. Since then, FBSDEs have been developed fastly and found many applications in kinds of fields such as PDEs [6,18], stochastic optimal control [11,16], mathematical finance [5], mean-field BSDEs [4,21,22] and stochastic differential games [9], etc. Hence the study on the numerical methods for solving FBSDEs needs much attention.…”

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confidence: 99%

Explicit multistep stochastic characteristic approximation methods for forward backward stochastic differential equations

Liu¹,

Sun²,

Zhang³

2022

DCDS-S

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<p style='text-indent:20px;'>In this work, by combining with stochastic approximation methods, we proposed a new explicit multistep scheme for solving the forward backward stochastic differential equations. Compared with the one constructed by using derivative approximation method, the new one covers the approximation of the stochastic part and is more accurate and easier to realize. Several numerical tests are presented to show the stability and effectiveness of the proposed scheme.</p>

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Explicit theta-Schemes for Mean-Field Backward Stochastic Differential Equations

Cited by 16 publications

References 18 publications

Backward-forward linear-quadratic mean-field Stackelberg games

Backward-forward linear-quadratic mean-field Stackelberg games

Explicit High Order One-Step Methods for Decoupled Forward Backward Stochastic Differential Equations

Explicit multistep stochastic characteristic approximation methods for forward backward stochastic differential equations

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