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Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis

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  • Vatamidou, E.
  • Adan, I.J.B.F.
  • Vlasiou, M.
  • Zwart, B.

Abstract

Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative errors. Motivated by statistical analysis, we assume that the claim sizes are a mixture of a phase-type and a heavy-tailed distribution and with the aid of perturbation analysis we derive a series expansion for the performance measure under consideration. Our proposed approximations consist of the first two terms of this series expansion, where the first term is a phase-type approximation of our measure. We refer to our approximations collectively as corrected phase-type approximations. We show that the corrected phase-type approximations exhibit a nice behavior both in finite and infinite time horizon, and we check their accuracy through numerical experiments.

Suggested Citation

  • Vatamidou, E. & Adan, I.J.B.F. & Vlasiou, M. & Zwart, B., 2013. "Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 366-378.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:2:p:366-378
    DOI: 10.1016/j.insmatheco.2013.07.002
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    References listed on IDEAS

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    Cited by:

    1. Peralta, Oscar & Rojas-Nandayapa, Leonardo & Xie, Wangyue & Yao, Hui, 2018. "Approximation of ruin probabilities via Erlangized scale mixtures," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 136-156.
    2. Hansjörg Albrecher & Martin Bladt & Eleni Vatamidou, 2021. "Efficient Simulation of Ruin Probabilities When Claims are Mixtures of Heavy and Light Tails," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1237-1255, December.
    3. Geiger Daniel J. & Adekpedjou Akim, 2019. "On corrected phase-type approximations of the time value of ruin with heavy tails," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 57-75, December.
    4. Josef Anton Strini & Stefan Thonhauser, 2020. "On Computations in Renewal Risk Models—Analytical and Statistical Aspects," Risks, MDPI, vol. 8(1), pages 1-20, March.

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