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An Outline of a Generalization — started by E. Sparre Andersen — of the classical Ruin Theory

Published online by Cambridge University Press:  29 August 2014

Olof Thorin
Olof Thorin*
Affiliation:
Stockholm
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E. Sparre Andersen [1]) presented to the XVth International Congress of Actuaries, New York, 1957, a model of a collective risk process with a positive gross risk premium where the epochs of claims formed a renewal process. Let Ψ(u) (where u denotes the original risk reserve) denote the ruin probability in this model. Generalizing the classical result Sparre Andersen deduced the inequality

where R is a suitable positive number depending on the distribution function (continuous to the right), P(y), — ∞ < y < ∞, P(o) < 1, for the amounts of claims in case a claim occurs and also depending on the distribution function, K(t), t > o, K(o) = o, for the times between the epochs of successive claims, (The times between the epochs of successive claims, the inter-occurrence times, are assumed to be independent and identically distributed random variables. The time between the starting point and the epoch of the first claim is assumed to be independent of and to have the same distribution function as the inter-occurrence times. The amounts of claims are assumed to be independent of each other and of the epochs of claims and to be identically distributed.)

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 6 , Issue 2 , December 1971 , pp. 108 - 115
Copyright
Copyright © International Actuarial Association 1971

References

[1]Andersen, E. Sparre, 1957: On the collective theory of risk in the case of contagion between the claims. Transactions XVth International Congress of Actuaries, New York, vol. II, 219–229.Google Scholar
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