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Approximations for the moments of ruin time in the compound Poisson model

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  • Pitts, Susan M.
  • Politis, Konstadinos

Abstract

In the classical risk model with Poisson arrivals, we study a functional approach which can be used to obtain new approximation formulae for the moments of the time to ruin. We explain how establishing differentiability of a functional, in appropriate function spaces, may lead to approximations for these moments. We consider various choices for the function spaces, which are suitable both for heavy-tailed and light-tailed claim-size distributions. The results are illustrated by some particular examples.

Suggested Citation

  • Pitts, Susan M. & Politis, Konstadinos, 2008. "Approximations for the moments of ruin time in the compound Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 668-679, April.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:668-679
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    References listed on IDEAS

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    1. Pitts, Susan M., 2004. "A Functional Approach to Approximations for the Individual Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 34(2), pages 379-397, November.
    2. Lin, X. Sheldon & Willmot, Gordon E., 2000. "The moments of the time of ruin, the surplus before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 19-44, August.
    3. Delbaen, Freddy, 1990. "A remark on the moments of ruin time in classical risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 121-126, September.
    4. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, October.
    5. Politis, Konstadinos & Pitts, Susan M., 1998. "Approximations for solutions of renewal-type equations," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 195-216, November.
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    Cited by:

    1. Lee, Wing Yan & Willmot, Gordon E., 2014. "On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 1-10.
    2. Vaios Dermitzakis & Konstadinos Politis, 2011. "Asymptotics for the Moments of the Time to Ruin for the Compound Poisson Model Perturbed by Diffusion," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 749-761, December.
    3. Philipp Lukas Strietzel & Anita Behme, 2022. "Moments of the Ruin Time in a Lévy Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3075-3099, December.
    4. Chi, Yichun & Jaimungal, Sebastian & Lin, X. Sheldon, 2010. "An insurance risk model with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 52-66, February.
    5. Jiechang Ruan & Wenguang Yu & Ke Song & Yihan Sun & Yujuan Huang & Xinliang Yu, 2019. "A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model," Mathematics, MDPI, vol. 7(10), pages 1-12, September.

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