Solving Coupled Nonlinear Forward-backward Stochastic Differential Equations: An Optimization Perspective with Backward Measurability Loss

Yutian Wang; Yuan-Hua Ni; Xun Li

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arXiv · 2310.13562

Solving Coupled Nonlinear Forward-backward Stochastic Differential Equations: An Optimization Perspective with Backward Measurability Loss

Yutian Wang·Yuan-Hua Ni·Xun Li

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Abstract

This paper aims to extend the BML method proposed in Wang et al. [22] to make it applicable to more general coupled nonlinear FBSDEs. We interpret BML from the fixed-point iteration perspective and show that optimizing BML is equivalent to minimizing the distance between two consecutive trial solutions in a fixed-point iteration. Thus, this paper provides a theoretical foundation for an optimization-based approach to solving FBSDEs. We also empirically evaluate the method through four numerical experiments.

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Yutian Wang, Yuan-Hua Ni, Xun Li. 2023-10-20. Solving Coupled Nonlinear Forward-backward Stochastic Differential Equations: An Optimization Perspective with Backward Measurability Loss. https://arxiv.org/abs/2310.13562

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