A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential Equation
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 investi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-05-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/9/1504 |
| Summary: | 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. |
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| ISSN: | 2227-7390 |