Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains
In this paper, we investigate the impact of the accident reporting strategy of drivers, within a Bonus-Malus system. We exhibit the induced modification of the corresponding class level transition matrix and derive the optimal reporting strategy for rational drivers. The hunger for bonuses induces o...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-11-01
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| Series: | Risks |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-9091/5/4/58 |
| _version_ | 1811270109574987776 |
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| author | Arthur Charpentier Arthur David Romuald Elie |
| author_facet | Arthur Charpentier Arthur David Romuald Elie |
| author_sort | Arthur Charpentier |
| collection | DOAJ |
| description | In this paper, we investigate the impact of the accident reporting strategy of drivers, within a Bonus-Malus system. We exhibit the induced modification of the corresponding class level transition matrix and derive the optimal reporting strategy for rational drivers. The hunger for bonuses induces optimal thresholds under which, drivers do not claim their losses. Mathematical properties of the induced level class process are studied. A convergent numerical algorithm is provided for computing such thresholds and realistic numerical applications are discussed. |
| first_indexed | 2024-04-12T21:55:22Z |
| format | Article |
| id | doaj.art-5bdd52de07704c318250e6ff49be04a7 |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-04-12T21:55:22Z |
| publishDate | 2017-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-5bdd52de07704c318250e6ff49be04a72022-12-22T03:15:20ZengMDPI AGRisks2227-90912017-11-01545810.3390/risks5040058risks5040058Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov ChainsArthur Charpentier0Arthur David1Romuald Elie2Faculte des Sciences Economiques, Universite Rennes 1, 7 Place Hoche, 35065 Rennes CEDEX, FranceFaculte des Sciences Economiques, Universite Rennes 1, 7 Place Hoche, 35065 Rennes CEDEX, FranceBatiment Bois de l’Etang, Universite Paris Est, 5 rue Galilee, 77420 Champs sur Marne, FranceIn this paper, we investigate the impact of the accident reporting strategy of drivers, within a Bonus-Malus system. We exhibit the induced modification of the corresponding class level transition matrix and derive the optimal reporting strategy for rational drivers. The hunger for bonuses induces optimal thresholds under which, drivers do not claim their losses. Mathematical properties of the induced level class process are studied. A convergent numerical algorithm is provided for computing such thresholds and realistic numerical applications are discussed.https://www.mdpi.com/2227-9091/5/4/58bonus hungerbonus-maluscontrolincentivesMarkov Chainsreporting |
| spellingShingle | Arthur Charpentier Arthur David Romuald Elie Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains Risks bonus hunger bonus-malus control incentives Markov Chains reporting |
| title | Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains |
| title_full | Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains |
| title_fullStr | Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains |
| title_full_unstemmed | Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains |
| title_short | Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains |
| title_sort | optimal claiming strategies in bonus malus systems and implied markov chains |
| topic | bonus hunger bonus-malus control incentives Markov Chains reporting |
| url | https://www.mdpi.com/2227-9091/5/4/58 |
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