Extremes on the discounted aggregate claims in a time dependent risk model

Article English OPEN
Asimit, A.V. ; Badescu, A. (2010)

This paper presents an extension of the classical compound Poisson risk model for which the inter-claim time and the forthcoming claim amount are no longer independent random variables (rv's). Asymptotic tail probabilities for the discounted aggregate claims are presented when the force of interest is constant and the claim amounts are heavy tail distributed rv's. Furthermore, we derive asymptotic finite time ruin probabilities, as well as asymptotic approximations for some common risk measures associated with the discounted aggregate claims. A simulation study is performed in order to validate the results obtained in the free interest risk model.
  • References (25)
    25 references, page 1 of 3

    Acerbi, C. and Tasche, D. 2002. “On the Coherence of Expected Shortfall,” Journal of Banking and Finance, 26(7), 1487-1503.

    Albrecher, H. and Boxma, O.J. 2004. “A Ruin Model with Dependence between Claim Sizes and Claim Intervals,” Insurance: Mathematics and Economics, 35(1), 245-254.

    Albrecher, H. and Boxma, O. 2005. “On the Discounted Penalty Function in a MarkovDependent Risk Model”, Insurance: Mathematics and Economics, 37(3), 650-672.

    Albrecher, H. and Teugels, J.L. 2006. “Exponential Behavior in the Presence of Dependence in Risk Theory,” Journal of Applied Probability, 43(1), 257-273.

    Alink, S. , L¨owe, M. and Wu¨thrich, M.V. 2005. “Analysis of the Expected Shortfall of Aggregate Dependent Risks,” ASTIN Bulletin, 35(1), 25-43.

    Asimit, A.V. and Jones, B.L. 2007. “Dependence and the Asymptotic Behavior of Large Claims Reinsurance,” submitted.

    Bingham, N.H., Goldie, C.M., and Teugels, J.L. 1987. Regular Variation. Cambridge University Press, Cambridge.

    Boudreault, M., Cossette, H., Landriault, D. and Marceau, E. 2006. “On a Risk Model with Dependence between Interclaim Arrivals and Claim Sizes,” Scandinavian Actuarial Journal, 5, 265-285.

    Cline, D.B.H. 1986. “Convolutions Tails, Product Tails and Domains of Attraction,” Probability Theory and Related Fields, 72(4), 529-557.

    Embrechts, P., Klu¨ppelberg, C. and Mikosch, T. 1997. Modelling Extremal Events for Insurance and Finance. Springer-Verlag, Berlin.

  • Metrics
    views in OpenAIRE
    views in local repository
    downloads in local repository

    The information is available from the following content providers:

    From Number Of Views Number Of Downloads
    City Research Online - IRUS-UK 0 47
Share - Bookmark