The moments of the time of ruin in Sparre Andersen risk models
We derive formulae for the moments of the time of ruin in both ordinary and modified Sparre Andersen risk models without specifying either the inter-claim time distribution or the individual claim amount distribution. We illustrate the application of our results in the special case of exponentially...
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Published in | Annals of actuarial science Vol. 17; no. 1; pp. 63 - 82 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Cambridge, UK
Cambridge University Press
01.03.2023
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Subjects | |
Online Access | Get full text |
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Summary: | We derive formulae for the moments of the time of ruin in both ordinary and modified Sparre Andersen risk models without specifying either the inter-claim time distribution or the individual claim amount distribution. We illustrate the application of our results in the special case of exponentially distributed claims, as well as for the following ordinary models: the classical risk model, phase-type(2) risk models, and the Erlang(
$\mathscr{n}$
) risk model. We also show how the key quantities for modified models can be found. |
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ISSN: | 1748-4995 1748-5002 |
DOI: | 10.1017/S1748499522000124 |