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INSURANCE RISK WITH VARIABLE NUMBER OF POLICIES

Published online by Cambridge University Press:  19 March 2008

Ivo Adan  and
Vidyadhar Kulkarni
Ivo Adan
Affiliation:
Department of Mathematics and Computer ScienceTechnische Universiteit Eindhoven5600 MB, Eindhoven, The Netherlands E-mail: [email protected]
Vidyadhar Kulkarni
Affiliation:
Department of Statistics and Operations ResearchUniversity of North CarolinaChapel Hill, NC, 27599 E-mail: [email protected]
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Abstract

In this article we consider an insurance company selling life insurance policies. New policies are sold at random points in time, and each policy stays active for an exponential amount of time with rate μ, during which the policyholder pays premiums continuously at rate r. When the policy expires, the insurance company pays a claim of random size. The aim is to compute the probability of eventual ruin starting with a given number of policies and a given level of insurance fund. We establish the remarkable result that the ruin probability is identical to the one in the standard compound Poisson model where the insurance fund increases at constant rate r and claims occur according to a Poisson process with rate μ.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 2 , March 2008 , pp. 213 - 219
Copyright
Copyright © Cambridge University Press 2008

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References

1.Rolski, T., Schmidli, H., Schmidt, V., & Teugels, J. (1999). Stochastic Processes for Insurance and Finance. Chichester: Wiley.CrossRefGoogle Scholar