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A new De Vylder type approximation of the ruin probability in infinite time

Author

Listed:
  • Krzysztof Burnecki
  • Pawel Mista
  • Aleksander Weron

Abstract

In this paper we introduce a generalization of the De Vylder approximation. Our idea is to approximate the ruin probability with the one for a different process with gamma claims, matching first four moments. We compare the two approximations studying mixture of exponentials and lognormal claims. In order to obtain exact values of the ruin probability for the lognormal case we use Pollaczeck-Khinchine formula. We show that the proposed 4-moment gamma De Vylder approximation works even better than the original one.

Suggested Citation

  • Krzysztof Burnecki & Pawel Mista & Aleksander Weron, 2003. "A new De Vylder type approximation of the ruin probability in infinite time," HSC Research Reports HSC/03/05, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    • Handle: RePEc:wuu:wpaper:hsc0305
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    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_03_05.pdf
    File Function: Original version, 2003
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    Citations

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    Cited by:

    1. David J. Santana & Juan González-Hernández & Luis Rincón, 2017. "Approximation of the Ultimate Ruin Probability in the Classical Risk Model Using Erlang Mixtures," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 775-798, September.

    More about this item

    Keywords

    Risk process; Ruin probability; De Vylder approximation; Pollaczeck-Khinchine formula;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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