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Asymptotics for the Moments of the Time to Ruin for the Compound Poisson Model Perturbed by Diffusion

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  • Vaios Dermitzakis

    (University of Piraeus)

  • Konstadinos Politis

    (University of Piraeus)

Abstract

We obtain the asymptotic behaviour of the k-th moment of the time to ruin in the classical risk model perturbed by diffusion for the case where the claim size distribution has a heavy tail.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:4:d:10.1007_s11009-010-9185-8
    DOI: 10.1007/s11009-010-9185-8
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    References listed on IDEAS

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    1. Dufresne, Francois & Gerber, Hans U., 1991. "Risk theory for the compound Poisson process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 51-59, March.
    2. Drekic, Steve & Stafford, James E. & Willmot, Gordon E., 2004. "Symbolic calculation of the moments of the time of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 109-120, February.
    3. 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.
    4. Veraverbeke, Noel, 1993. "Asymptotic estimates for the probability of ruin in a Poisson model with diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 13(1), pages 57-62, September.
    5. 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.
    6. Tsai, Cary Chi-Liang & Willmot, Gordon E., 2002. "On the moments of the surplus process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 327-350, December.
    7. 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.
    8. Egidio dos Reis, Alfredo D., 2000. "On the moments of ruin and recovery times," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 331-343, December.
    9. Picard, Philippe & Lefevre, Claude, 1998. "The moments of ruin time in the classical risk model with discrete claim size distribution," Insurance: Mathematics and Economics, Elsevier, vol. 23(2), pages 157-172, November.
    10. Vaios Dermitzakis & Susan M. Pitts & Konstadinos Politis, 2010. "Lundberg-type Bounds and Asymptotics for the Moments of the Time to Ruin," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 155-175, March.
    11. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
    12. Dickson, David C.M. & Willmot, Gordon E., 2005. "The Density of the Time to Ruin in the Classical Poisson Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 45-60, May.
    13. Drekic, Steve & Willmot, Gordon E., 2003. "On the Density and Moments of the Time of Ruin with Exponential Claims," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 11-21, May.
    14. Steve Drekic & Gordon Willmot, 2005. "On the Moments of the Time of Ruin with Applications to Phase-Type Claims," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(2), pages 17-30.
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