Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach
This paper is concerned with an insurance risk model whose claim process is described by a Lévy subordinator process. Lévy-type risk models have been the object of much research in recent years. Our purpose is to present, in the case of a subordinator, a simple and direct method for determining the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-12-01
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| Series: | Risks |
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| Online Access: | http://www.mdpi.com/2227-9091/1/3/192 |
| _version_ | 1819047813318705152 |
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| author | Claude Lefèvre Philippe Picard |
| author_facet | Claude Lefèvre Philippe Picard |
| author_sort | Claude Lefèvre |
| collection | DOAJ |
| description | This paper is concerned with an insurance risk model whose claim process is described by a Lévy subordinator process. Lévy-type risk models have been the object of much research in recent years. Our purpose is to present, in the case of a subordinator, a simple and direct method for determining the finite time (and ultimate) ruin probabilities, the distribution of the ruin severity, the reserves prior to ruin, and the Laplace transform of the ruin time. Interestingly, the usual net profit condition will be essentially relaxed. Most results generalize those known for the compound Poisson claim process. |
| first_indexed | 2024-12-21T11:06:19Z |
| format | Article |
| id | doaj.art-797a99de5fcf42b4835829d1a85219b0 |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-12-21T11:06:19Z |
| publishDate | 2013-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-797a99de5fcf42b4835829d1a85219b02022-12-21T19:06:13ZengMDPI AGRisks2227-90912013-12-011319221210.3390/risks1030192risks1030192Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple ApproachClaude Lefèvre0Philippe Picard1Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, Bruxelles B-1050, BelgiumInstitut de Science Financière et d'Assurances, Université de Lyon, 50 Avenue Tony Garnier, Lyon F-69007, FranceThis paper is concerned with an insurance risk model whose claim process is described by a Lévy subordinator process. Lévy-type risk models have been the object of much research in recent years. Our purpose is to present, in the case of a subordinator, a simple and direct method for determining the finite time (and ultimate) ruin probabilities, the distribution of the ruin severity, the reserves prior to ruin, and the Laplace transform of the ruin time. Interestingly, the usual net profit condition will be essentially relaxed. Most results generalize those known for the compound Poisson claim process.http://www.mdpi.com/2227-9091/1/3/192Lévy subordinatortime reversalruin probability(in)finite time horizonruin severityreserves prior to ruinruin time |
| spellingShingle | Claude Lefèvre Philippe Picard Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach Risks Lévy subordinator time reversal ruin probability (in)finite time horizon ruin severity reserves prior to ruin ruin time |
| title | Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach |
| title_full | Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach |
| title_fullStr | Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach |
| title_full_unstemmed | Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach |
| title_short | Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach |
| title_sort | ruin time and severity for a levy subordinator claim process a simple approach |
| topic | Lévy subordinator time reversal ruin probability (in)finite time horizon ruin severity reserves prior to ruin ruin time |
| url | http://www.mdpi.com/2227-9091/1/3/192 |
| work_keys_str_mv | AT claudelefevre ruintimeandseverityforalevysubordinatorclaimprocessasimpleapproach AT philippepicard ruintimeandseverityforalevysubordinatorclaimprocessasimpleapproach |