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 |
| _version_ | 1797503858808717312 |
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| author | Bihao Su Chenglong Xu Jingchao Li |
| author_facet | Bihao Su Chenglong Xu Jingchao Li |
| author_sort | Bihao Su |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T03:56:23Z |
| format | Article |
| id | doaj.art-306aae38fe004ece8b7ffa0e7195cd9d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:56:23Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-306aae38fe004ece8b7ffa0e7195cd9d2023-11-23T08:45:22ZengMDPI AGMathematics2227-73902022-05-01109150410.3390/math10091504A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential EquationBihao Su0Chenglong Xu1Jingchao Li2School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, ChinaSchool of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, ChinaCollege of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, ChinaIn 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.https://www.mdpi.com/2227-7390/10/9/1504deep neural networkpartial integro-differential equationsurvival probabilityGeneralized Simpson rulenetwork function |
| spellingShingle | Bihao Su Chenglong Xu Jingchao Li A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential Equation Mathematics deep neural network partial integro-differential equation survival probability Generalized Simpson rule network function |
| title | A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential Equation |
| title_full | A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential Equation |
| title_fullStr | A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential Equation |
| title_full_unstemmed | A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential Equation |
| title_short | A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential Equation |
| title_sort | deep neural network approach to solving for seal s type partial integro differential equation |
| topic | deep neural network partial integro-differential equation survival probability Generalized Simpson rule network function |
| url | https://www.mdpi.com/2227-7390/10/9/1504 |
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