An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company
Catastrophe is a loss that has a low probability of occurring but can lead to high-cost claims. This paper uses the data of fire accidents from a reinsurance company in Thailand for an experiment. Our study is in two parts. First, we approximate the parameters of a Weibull distribution. We compare t...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2019/2191509 |
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| author | Soontorn Boonta Somchit Boonthiem |
| author_facet | Soontorn Boonta Somchit Boonthiem |
| author_sort | Soontorn Boonta |
| collection | DOAJ |
| description | Catastrophe is a loss that has a low probability of occurring but can lead to high-cost claims. This paper uses the data of fire accidents from a reinsurance company in Thailand for an experiment. Our study is in two parts. First, we approximate the parameters of a Weibull distribution. We compare the parameter estimation using a direct search method with other frequently used methods, such as the least squares method, the maximum likelihood estimation, and the method of moments. The results show that the direct search method approximates the parameters more precisely than other frequently used methods (to four-digit accuracy). Second, we approximate the minimum initial capital (MIC) a reinsurance company has to hold under a given ruin probability (insolvency probability) by using parameters from the first part. Finally, we show MIC with varying the premium rate. |
| format | Article |
| id | doaj-art-c2e059742502402388b715722e15a5c3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c2e059742502402388b715722e15a5c32025-02-03T01:03:27ZengWileyJournal of Applied Mathematics1110-757X1687-00422019-01-01201910.1155/2019/21915092191509An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance CompanySoontorn Boonta0Somchit Boonthiem1Department of General Science, Faculty of Science and Engineering, Kasetsart University, Chalermphrakiat Sakon Nakhon Province Campus, Sakon Nakhon 47000, ThailandMathematics and Statistics Program, Faculty of Science, Sakon Nakhon Rajabhat University, Sakon Nakhon 47000, ThailandCatastrophe is a loss that has a low probability of occurring but can lead to high-cost claims. This paper uses the data of fire accidents from a reinsurance company in Thailand for an experiment. Our study is in two parts. First, we approximate the parameters of a Weibull distribution. We compare the parameter estimation using a direct search method with other frequently used methods, such as the least squares method, the maximum likelihood estimation, and the method of moments. The results show that the direct search method approximates the parameters more precisely than other frequently used methods (to four-digit accuracy). Second, we approximate the minimum initial capital (MIC) a reinsurance company has to hold under a given ruin probability (insolvency probability) by using parameters from the first part. Finally, we show MIC with varying the premium rate.http://dx.doi.org/10.1155/2019/2191509 |
| spellingShingle | Soontorn Boonta Somchit Boonthiem An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company Journal of Applied Mathematics |
| title | An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company |
| title_full | An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company |
| title_fullStr | An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company |
| title_full_unstemmed | An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company |
| title_short | An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company |
| title_sort | approximation of minimum initial capital of investment discrete time surplus process with weibull distribution in a reinsurance company |
| url | http://dx.doi.org/10.1155/2019/2191509 |
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