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Impact of underwriting cycles on the solvency of an insurance company

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Trufin, Julien [UCL] Albrecher, Hansjörg [University of Lausanne] Denuit, Michel [UCL]

This paper studies the solvency of an insurance firm in the presence of underwriting cycles. A small or medium-size insurance company with a price-taker position in the market is considered. Its premium income is assumed to obey an autoregressive process with cycles. Specifically, the premium income for a specific calendar year is influenced by the market experience for the last couple years. Under this classical AR(2) dynamics governing the premium income, an explicit expression for the ultimate ruin probability is derived, using a martingale approach, in the lighttailed claims case. Furthermore, the logarithmic asymptotic behavior of the ultimate ruin probability as well as the typical path to ruin are investigated. Then a comparison is made with the classical case where the same company operates on a market without such cycles. Asymptotically, the presence of market cycles is shown to increase the risk for the company. Numerical illustrations are performed on Canadian motor insurance market data and support the theoretical analysis.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès interdit
Publication date 2009
Language Anglais
Journal information "North American Actuarial Journal" - Vol. 13, no.3, p. 385-403 (2009)
Peer reviewed yes
Publisher Society of Actuaries ((United States) Schaumburg)
issn 1092-0277
Publication status Publié
Affiliation UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Links
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Bibliographic reference Trufin, Julien ; Albrecher, Hansjörg ; Denuit, Michel. Impact of underwriting cycles on the solvency of an insurance company. In: North American Actuarial Journal, Vol. 13, no.3, p. 385-403 (2009)
Permanent URL http://hdl.handle.net/2078.1/125112