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Empirical bounds for ruin probabilities

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  • Grandell, Jan

Abstract

We consider the classical model for an insurance business where the claims occur according to a Poisson process and where the distribution for the cost of each claim fulfills Cramér's tail-condition. Under these conditions Lundberg's constant R is of fundamental importance for ruin calculations. We derive estimates of R, based on an observation of the insurance business and investigate the statistical properties of those estimates. We further derive bounds and confidence intervals for ruin probabilities.

Suggested Citation

  • Grandell, Jan, 1979. "Empirical bounds for ruin probabilities," Stochastic Processes and their Applications, Elsevier, vol. 8(3), pages 243-255, May.
    • Handle: RePEc:eee:spapps:v:8:y:1979:i:3:p:243-255
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    Cited by:

    1. Christ, Ralf & Steinebach, Josef, 1995. "Estimating the adjustment coefficient in an ARMA(p, q) risk model," Insurance: Mathematics and Economics, Elsevier, vol. 17(2), pages 149-161, October.
    2. Peng, Xiaofan & Chen, Mi & Guo, Junyi, 2012. "Optimal dividend and equity issuance problem with proportional and fixed transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 576-585.
    3. Gajek, Leslaw, 2005. "On the deficit distribution when ruin occurs--discrete time model," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 13-24, February.

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