A new efficient approximation scheme for solving high-dimensional semilinear PDEs: Control variate method for Deep BSDE solver

Takahashi, Akihiko; Tsuchida, Yoshifumi; Yamada, Toshihiro

doi:10.1016/j.jcp.2022.110956

Cited by 11 publications

(1 citation statement)

References 42 publications

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“…Additionally, we have presented a special example for a simple case. For future work, we will focus on this interesting problem and pay more attention to the simulation of numerical solutions of BSDEs of multidimensional and even infinite-dimensional types and their applications in finance and computing, such as [27][28][29].…”

Section: Discussionmentioning

confidence: 99%

Backward Stochastic Differential Equations (BSDEs) Using Infinite-Dimensional Martingales with Subdifferential Operator

Zhang

Ibrahim

Mohamed

2022

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In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with subdifferential operators that are driven by infinite-dimensional martingales. We shall show that the solution to such infinite-dimensional BSDEs exists and is unique. The existence and uniqueness of the solution are established using Yosida approximations. Furthermore, as an application of the main result, we shall show that the backward stochastic partial differential equation driven by infinite-dimensional martingales with a continuous linear operator has a unique solution under the special condition that the Ft-progressively measurable generator F of the model we proposed in this paper equals zero.

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Section: Discussionmentioning

confidence: 99%