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

Edward Furman, Daniel Hackmann and Alexey Kuznetsov

Insurance: Mathematics and Economics, 2020, vol. 90, issue C, 120-134

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.

Keywords: Log-normal distribution; Convolution; Generalized gamma convolution; Padé approximation; Individual risk model; Collective risk model; Economic capital (search for similar items in EconPapers)
JEL-codes: C02 C46 C63 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.insmatheco.2019.10.003

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