Deep Signature FBSDE Algorithm

Qi Feng, Man Luo and Zhaoyu Zhang

Papers from arXiv.org

Abstract: We propose a deep signature/log-signature FBSDE algorithm to solve forward-backward stochastic differential equations (FBSDEs) with state and path dependent features. By incorporating the deep signature/log-signature transformation into the recurrent neural network (RNN) model, our algorithm shortens the training time, improves the accuracy, and extends the time horizon comparing to methods in the existing literature. Moreover, our algorithms can be applied to a wide range of applications such as state and path dependent option pricing involving high-frequency data, model ambiguity, and stochastic games, which are linked to parabolic partial differential equations (PDEs), and path-dependent PDEs (PPDEs). Lastly, we also derive the convergence analysis of the deep signature/log-signature FBSDE algorithm.

Date: 2021-08, Revised 2022-08
New Economics Papers: this item is included in nep-big, nep-cmp, nep-gth, nep-isf and nep-ore
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