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Ruin probabilities expressed in terms of storage processes

Published online by Cambridge University Press:  01 July 2016

Søren Asmussen  and
Søren Schock Petersen
Søren Asmussen*
Affiliation:
Aalborg University
Søren Schock Petersen*
Affiliation:
The Danish State Life Insurance Company
*
∗Postal address: Institute of Electronic Systems, Aalborg University, Strandvejen 19, DK-9000 Aalborg, Denmark.
∗∗Postal address: Statsanstalten for Livsforsikring, Kampmannsgade 4, DK-1645 København V, Denmark.
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Abstract

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It is shown by a simple sample path argument that the ruin probabilities for a risk reserve process with premium rate p(r) depending on the reserve r and finite or infinite horizon are related in a simple way to the state probabilities of a compound Poisson dam with the same release rate p(r) at content r. In the infinite horizon case, this result has been established by Harrison and Resnick (1978), and in the finite horizon case with constant p it extends well-known relations to the M/G/1 virtual waiting time.

Keywords

FINITE HORIZONSAMPLE PATH COMPARISON
Type
Letter to the Editor
Information
Advances in Applied Probability , Volume 20 , Issue 4 , December 1988 , pp. 913 - 916
Copyright
Copyright © Applied Probability Trust 1988 

Footnotes

Research partly carried out while this author was visiting the University of California, Santa Barbara.

References

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