Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T16:49:41.468Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1] Asmussen, S. (1987) Applied Probability and Queues. Wiley, Chichester.Google Scholar
[2] Baker, C. T. H. (1977) The Numerical Solution of Integral Equations. Clarendon Press, Oxford.Google Scholar
[3] Brockwell, P. J., Resnick, S. I. and Tweedie, R. L. (1982) Storage processes with general release rule and additive inputs. Adv. Appl. Prob. 14, 392–433.CrossRefGoogle Scholar
[4] Gerber, H. (1971) Der Einfluss von Zins auf die Ruinwahrscheinlichkeit. Mitt. Verein Schweiz. Versich. Math. 71, 63–70.Google Scholar
[5] Harrison, J. M. (1977) Ruin problems with compounding assets. Stoch. Proc. Appl. 5, 67–79.CrossRefGoogle Scholar
[6] Harrison, J. M. and Resnick, S. I. (1976) The stationary distribution and first exit probabilities of a storage process with general release rule. Math. Operat. Res. 1, 347–358.Google Scholar
[7] Harrison, J. M. and Resnick, S. I. (1978) The recurrence classification of risk and storage processes. Math. Operat Res. 3, 57–66.Google Scholar
[8] Prabhu, N. U. (1961) On the ruin problem of collective risk theory. Ann. Math. Statist. 32, 757–764.Google Scholar
[9] Prabhu, N. U. (1980) Stochastic Storage Processes. Queues, Insurance Risk, and Dams. Springer-Verlag, New York.CrossRefGoogle Scholar
[10] Schock Petersen, S. (1988) Calculation of ruin probabilities when the premium depends on the current reserve. Submitted.Google Scholar
[11] Seal, H. L. (1972) Risk theory and the single server queue. Mitt. Verein Schweiz. Versich. Math. 72, 171–178.Google Scholar