2023/01/30 by Wansheng Wang, Jie Wang, Wang, Wansheng +7 · 2 citations
Economics, Econometrics and Finance · Engineering · #60H10 #60H35 #65C20 #65C30 #65M15 #65M75 #Energy Load and Power Forecasting #FOS: Computer and information sciences #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2301.12895
openalex publication_date 2023/01/30 · openalex created_date 2023/02/01 · openalex updated_date 2026/07/28
We propose a deep learning algorithm for solving high-dimensional parabolic integro-differential equations (PIDEs) and high-dimensional forward-backward stochastic differential equations with jumps (FBSDEJs), where the jump-diffusion process are derived by a Brownian motion and an independent compensated Poisson random measure. In this novel algorithm, a pair of deep neural networks for the approximations of the gradient and the integral kernel is introduced in a crucial way based on deep FBSDE method. To derive the error estimates for this deep learning algorithm, the convergence of Markovian iteration, the error bound of Euler time discretization, and the simulation error of deep learning algorithm are investigated. Two numerical examples are provided to show the efficiency of this proposed algorithm.