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Asimit, A.V.; Badescu, A. (2010)
Languages: English
Types: Article
Subjects: HG
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.
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    • 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.
    • Gnedenko, B.V. 1943. “Sur la Distribution Limit´e du Terme Maximum d'une S´erie Al´eatoaire,” Annals of Mathematics, 44, 423-453.
    • Goldie, C.M. and Resnick, S.I. 1988. “Distributions that are both Subexponential and in the Domain of Attraction of an extreme-Value Distribution,” Advances in Applied Probability, 20(4), 706-718.
    • Jorion, P. 2001. Value-at-Risk, McGraw-Hill, New York.
    • Ladoucette, S.A. and Teugels, J.L. 2006. “Reinsurance of Large Claims,” Journal of Computational and Applied Mathematics, 186(1), 163-190.
    • McNeil, A.J., Frey, R. and Embrechts, P. 2005. Quantative Risk Management: Concepts, Techniques and Tools. Princeton University Press, Princeton.
    • Nelsen, R. B. 1999. An Introduction to Copulas. Springer-Verlag, New York.
    • Pratt, J.W. 1960. “On Interchanging limits and integrals,” Annals of Mathematical Statistics, 31(1), 74-77.
    • Resnick, S.I. 1987. Extreme Values, Regular Variation and Point Processes. Springer-Verlag, New York.
    • Ronkainen, V., Koskinen, L. and Berglund, R. 2007. “Topical Modelling Issues in Solvency II,” Scandinavian Actuarial Journal, 2, 135-146.
    • Sklar, A. 1959. “Fonctions de r´epartion `a n dimensions et leurs marges,” Publications de l'Institut de Statistique de l'Universit´e de Paris, 8, 229-231.
    • Tang, Q. 2005a. “Asymptotic ruin probabilities of the renewal model with constant interest force and regular variation”, Scandinavian Actuarial Journal, 1, 1-5.
    • Tang, Q. 2005b. “The Finite Time Ruin Probability of the Compound Poisson Model with Constant Interest Force,” Journal of Applied Probability, 42(3), 608-619.
    • Tang, Q. 2007. “Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model,” Journal of Applied Probability, 44(2), 285-294.
    • Tasche, D. 2002. “Expected Shortfall and Beyond,” Journal of Banking and Finance, 26(7), 1519-1533.
    • Wang, D. 2008. “Finite Time Ruin Probability with Heavy-Tailed Claims and Constant Interest Rate,” Stochastic Models, 24(1), 41-57.
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