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Impact of Underwriting Cycles on the Solvency of an Insurance Company

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  • Julien Trufin
  • Hansjörg Albrecher
  • Michel Denuit

Abstract

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.

Suggested Citation

  • Julien Trufin & Hansjörg Albrecher & Michel Denuit, 2009. "Impact of Underwriting Cycles on the Solvency of an Insurance Company," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(3), pages 385-403.
    • Handle: RePEc:taf:uaajxx:v:13:y:2009:i:3:p:385-403
    DOI: 10.1080/10920277.2009.10597564
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    Cited by:

    1. Ronnie J. Phillips & David Nickerson, 2011. "Underwriting in Property-Casualty Insurance Markets: Regulation, Risk and Volatility," NFI Working Papers 2011-WP-19, Indiana State University, Scott College of Business, Networks Financial Institute.
    2. M. Martin Boyer, 2013. "Underwriting Apophenia and Cryptids: Are Cycles Statistical Figments of our Imagination?," CIRANO Working Papers 2013s-07, CIRANO.

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