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Ruin probability and time of ruin with a proportional reinsurance threshold strategy

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  • Anna Castañer
  • M. Claramunt
  • Maite Mármol

Abstract

In this paper, we present a threshold proportional reinsurance strategy and we analyze the effect on some solvency measures: ruin probability and time of ruin. This dynamic reinsurance strategy assumes a retention level that is not constant and depends on the level of the surplus. In a model with inter-occurrence times being generalized Erlang(n)-distributed, we obtain the integro-differential equation for the Gerber–Shiu function. Then, we present the solution for inter-occurrence times exponentially distributed and claim amount phase-type(N). Some examples for exponential and phase-type(2) claim amount are presented. Finally, we show some comparisons between threshold reinsurance and proportional reinsurance. Copyright Sociedad de Estadística e Investigación Operativa 2012

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  • Anna Castañer & M. Claramunt & Maite Mármol, 2012. "Ruin probability and time of ruin with a proportional reinsurance threshold strategy," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 614-638, October.
    • Handle: RePEc:spr:topjnl:v:20:y:2012:i:3:p:614-638
    DOI: 10.1007/s11750-010-0165-5
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    References listed on IDEAS

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    Cited by:

    1. Eva Boj del Val & M. Mercè Claramunt Bielsa & Xavier Varea Soler, 2020. "Role of Private Long-Term Care Insurance in Financial Sustainability for an Aging Society," Sustainability, MDPI, vol. 12(21), pages 1-21, October.
    2. Castañer, A. & Claramunt, M.M. & Lefèvre, C., 2013. "Survival probabilities in bivariate risk models, with application to reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 632-642.
    3. Anna Castañer & M.Mercè Claramunt & Maite Mármol, 2014. "Some optimization and decision problems in proportional reinsurance," UB School of Economics Working Papers 2014/310, University of Barcelona School of Economics.
    4. Sancho Salcedo-Sanz & L. Carro-Calvo & Mercè Claramunt & Anna Castañer & Maite Marmol, 2013. "An Analysis of Black-box Optimization Problems in Reinsurance: Evolutionary-based Approaches," Working Papers XREAP2013-04, Xarxa de Referència en Economia Aplicada (XREAP), revised May 2013.

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