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Determination of the probability of ultimate ruin by maximum entropy applied to fractional moments

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  • Gzyl, Henryk
  • Novi-Inverardi, Pier-Luigi
  • Tagliani, Aldo

Abstract

In this work we present two different numerical methods to determine the probability of ultimate ruin as a function of the initial surplus. Both methods use moments obtained from the Pollaczek–Kinchine identity for the Laplace transform of the probability of ultimate ruin. One method uses fractional moments combined with the maximum entropy method and the other is a probabilistic approach that uses integer moments directly to approximate the density.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:2:p:457-463
    DOI: 10.1016/j.insmatheco.2013.07.011
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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. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    3. 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. 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.
    2. Pierre-Olivier Goffard & Stéphane Loisel & Denys Pommeret, 2015. "A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model," Post-Print hal-00853680, HAL.
    3. 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.

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