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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Bibliographic Details
Published inAnnals of actuarial science Vol. 17; no. 1; pp. 63 - 82
Main Author Dickson, David C.M.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.03.2023
Subjects
Actuarial science
Equilibrium
Laplace transforms
Original Research Paper
Random variables
Time of ruin
Moments
Sparre Andersen model
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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.
ISSN:1748-4995
1748-5002
DOI:10.1017/S1748499522000124