Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem
It is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus, a loss function that measures the loss sustai...
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| Format: | Article |
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MDPI AG
2019-06-01
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| Series: | Risks |
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| Online Access: | https://www.mdpi.com/2227-9091/7/2/68 |
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| author | Emilio Gómez-Déniz José María Sarabia Enrique Calderín-Ojeda |
| author_facet | Emilio Gómez-Déniz José María Sarabia Enrique Calderín-Ojeda |
| author_sort | Emilio Gómez-Déniz |
| collection | DOAJ |
| description | It is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus, a loss function that measures the loss sustained by a decision-maker who takes as valid a ruin function which is not correct can be considered. By using squared-error loss function and appropriate distribution function for these parameters, the issue of estimating the ruin function derives in a mixture procedure. Firstly, a bivariate distribution for mixing jointly the two parameters is considered, and second, different univariate distributions for mixing both parameters separately are examined. Consequently, a catalogue of ruin probability functions and severity of ruin, which are more flexible than the original one, are obtained. The methodology is also extended to the Pareto claim size distribution. Several numerical examples illustrate the performance of these functions. |
| first_indexed | 2024-12-21T19:31:30Z |
| format | Article |
| id | doaj.art-ba3ba7e514e344ba81029a619b42acaa |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-12-21T19:31:30Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-ba3ba7e514e344ba81029a619b42acaa2022-12-21T18:52:42ZengMDPI AGRisks2227-90912019-06-01726810.3390/risks7020068risks7020068Ruin Probability Functions and Severity of Ruin as a Statistical Decision ProblemEmilio Gómez-Déniz0José María Sarabia1Enrique Calderín-Ojeda2Department of Quantitative Methods and Institute of Tourism and Sustainable Economic Development (TIDES), University of Las Palmas de Gran Canaria, E-35017 Las Palmas de Gran Canaria, SpainDepartment of Economics, University of Cantabria, E-39005 Santander, SpainCentre for Actuarial Studies, Department of Economics, The University of Melbourne, Melbourne, VIC 3010, AustraliaIt is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus, a loss function that measures the loss sustained by a decision-maker who takes as valid a ruin function which is not correct can be considered. By using squared-error loss function and appropriate distribution function for these parameters, the issue of estimating the ruin function derives in a mixture procedure. Firstly, a bivariate distribution for mixing jointly the two parameters is considered, and second, different univariate distributions for mixing both parameters separately are examined. Consequently, a catalogue of ruin probability functions and severity of ruin, which are more flexible than the original one, are obtained. The methodology is also extended to the Pareto claim size distribution. Several numerical examples illustrate the performance of these functions.https://www.mdpi.com/2227-9091/7/2/68loss functionexponential distributionpareto distributionruin functionseverity of ruinupper bound |
| spellingShingle | Emilio Gómez-Déniz José María Sarabia Enrique Calderín-Ojeda Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem Risks loss function exponential distribution pareto distribution ruin function severity of ruin upper bound |
| title | Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem |
| title_full | Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem |
| title_fullStr | Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem |
| title_full_unstemmed | Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem |
| title_short | Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem |
| title_sort | ruin probability functions and severity of ruin as a statistical decision problem |
| topic | loss function exponential distribution pareto distribution ruin function severity of ruin upper bound |
| url | https://www.mdpi.com/2227-9091/7/2/68 |
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