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On log-normal convolutions: An analytical–numerical method with applications to economic capital determination

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  • Furman, Edward
  • Hackmann, Daniel
  • Kuznetsov, Alexey

Abstract

We put forward an efficient algorithm for approximating the sums of independent and log-normally distributed random variables. Namely, by combining tools from probability theory and numerical analysis, we are able to compute the cumulative distribution functions of the just-mentioned sums to a high precision and in a relatively short computing time. We illustrate the effectiveness of the new method in the contexts of the individual and collective risk models, aggregate economic capital determination, and economic capital allocation.

Suggested Citation

  • Furman, Edward & Hackmann, Daniel & Kuznetsov, Alexey, 2020. "On log-normal convolutions: An analytical–numerical method with applications to economic capital determination," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 120-134.
    • Handle: RePEc:eee:insuma:v:90:y:2020:i:c:p:120-134
    DOI: 10.1016/j.insmatheco.2019.10.003
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    Cited by:

    1. Gao, Guangyuan, 2024. "Fitting Tweedie's compound Poisson model to pure premium with the EM algorithm," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 29-42.
    2. Boyle, Phelim & Jiang, Ruihong, 2023. "A note on portfolios of averages of lognormal variables," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 97-109.
    3. Mohammed, Nawaf & Furman, Edward & Su, Jianxi, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 425-436.
    4. Nawaf Mohammed & Edward Furman & Jianxi Su, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of Conditional Tail Expectation," Papers 2102.05003, arXiv.org, revised Aug 2021.

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    More about this item

    Keywords

    Log-normal distribution; Convolution; Generalized gamma convolution; Padé approximation; Individual risk model; Collective risk model; Economic capital;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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