A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential Equation

Bihao Su, Chenglong Xu and Jingchao Li
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Bihao Su: School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China
Chenglong Xu: School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China
Jingchao Li: College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China

Mathematics, 2022, vol. 10, issue 9, 1-21

Abstract: In this paper, we study the problem of solving Seal’s type partial integro-differential equations (PIDEs) for the classical compound Poisson risk model. A data-driven deep neural network (DNN) method is proposed to calculate finite-time survival probability, and an alternative scheme is also investigated when claim payments are exponentially distributed. The DNN method is then extended to the numerical solution of generalized PIDEs. Numerical approximation results under different claim distributions are given, which show that the proposed scheme can obtain accurate results under different claim distributions.

Keywords: deep neural network; partial integro-differential equation; survival probability; Generalized Simpson rule; network function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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