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Approximation of the ruin probability using the scaled Laplace transform inversion

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  • Mnatsakanov, Robert M.
  • Sarkisian, Khachatur
  • Hakobyan, Artak

Abstract

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen–Weideman–Schmelzer and maximum entropy methods are presented via a simulation study.

Suggested Citation

  • Mnatsakanov, Robert M. & Sarkisian, Khachatur & Hakobyan, Artak, 2015. "Approximation of the ruin probability using the scaled Laplace transform inversion," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 717-727.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:717-727
    DOI: 10.1016/j.amc.2015.06.087
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    References listed on IDEAS

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    1. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of distributions," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1612-1618, September.
    2. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    3. Gzyl, Henryk & Novi-Inverardi, Pier-Luigi & Tagliani, Aldo, 2013. "Determination of the probability of ultimate ruin by maximum entropy applied to fractional moments," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 457-463.
    4. Mnatsakanov, Robert M., 2011. "Moment-recovered approximations of multivariate distributions: The Laplace transform inversion," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 1-7, January.
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    Cited by:

    1. Pierre-Olivier Goffard & Stéphane Loisel & Denys Pommeret, 2017. "Polynomial Approximations for Bivariate Aggregate Claims Amount Probability Distributions," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 151-174, March.
    2. 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.
    3. Hu, Xiang & Duan, Baige & Zhang, Lianzeng, 2017. "De Vylder approximation to the optimal retention for a combination of quota-share and excess of loss reinsurance with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 48-55.

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