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Probabilities of ruin when the safety loading tends to zero

Part of: Limit theorems Mathematical economics

Published online by Cambridge University Press:  01 July 2016

Vsevolod K. Malinovskii
Vsevolod K. Malinovskii*
Affiliation:
Steklov Mathematical Institute
*
∗ Postal address: Steklov Mathematical Institute, Gubkina str 8, 117966 Moscow GSP-1, Russia. Email address: malinov@mi.ras.ru
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Abstract

When the premium rate is a positive absolute constant throughout the time period of observation and the safety loading of the insurance business is positive, a classical result of collective risk theory claims that probabilities of ultimate ruin ψ(u) and of ruin within finite time ψ(t,u) decrease as eϰu with a constant ϰ>0, as the initial risk reserve u increases. This paper establishes uniform approximations to ψ(t,u) with slower rates of decrease when the premium rate depends on u in such a way that the safety loading decreases to zero asu→∞.

Keywords

Ruin theoryAndersen's risk modelcapital-dependentsafety loadingsapproximations

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 60F99: None of the above, but in this section

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 3 , September 2000 , pp. 885 - 923
Copyright
Copyright © Applied Probability Trust 2000 

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