论文标题
深层分裂方案的收敛分析：部分间距分化方程和相关的FBSDE的情况
Convergence Analysis of the Deep Splitting Scheme: the Case of Partial Integro-Differential Equations and the associated FBSDEs with Jumps
论文作者
论文摘要
高维抛物线部分局部差异方程（pides）出现在保险和金融的许多应用中。现有的数值方法遭受维数的诅咒或仅针对给定的时空点提供解决方案。这引起了关于解决部分微分方程的基于深度学习的方法的越来越多的文献。另一方面，整数差异方程的结果很少。在本文中，我们考虑了由于贝克，贝克，贝克，切里迪托，詹森，诺伊费尔德（2021）和吉安，帕林（2022）（2022年）引起的深层分裂方案的扩展。我们的主要贡献是对该方案的收敛分析。此外，我们讨论了一些测试案例研究，以显示我们方法的可行性。
High-dimensional parabolic partial integro-differential equations (PIDEs) appear in many applications in insurance and finance. Existing numerical methods suffer from the curse of dimensionality or provide solutions only for a given space-time point. This gave rise to a growing literature on deep learning based methods for solving partial differential equations; results for integro-differential equations on the other hand are scarce. In this paper we consider an extension of the deep splitting scheme due to Beck, Becker, Cheridito, Jentzen, Neufeld (2021) and Germain, Pham, Warin (2022) to PIDEs. Our main contribution is a convergence analysis of the scheme. Moreover we discuss several test case studies to show the viability of our approach.
