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Diffusion approximations in collective risk theory

Published online by Cambridge University Press:  14 July 2016

L. Donald Iglehart
L. Donald Iglehart*
Affiliation:
Stanford University
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Extract

Collective risk theory is concerned with the random fluctations of the total assets, the risk reserve, of an insurance company. Consider a company which only writes ordinary insurance policies such as accident, disability, fire, health, and whole life. The policyholders pay premiums regularly and at certain random times make claims to the company. A policyholder's premium, the gross risk premium, is a positive amount composed of two components. The net risk premium is the component calculated to cover the payments of claims on the average, while the security risk premium, or safety loading, is the component which protects the company from large deviations of claims from the average and also allows an accumulation of capital. When a claim occurs the company pays the policyholder a positive amount called the positive risk sum.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 2 , August 1969 , pp. 285 - 292
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Billingsley, P. (1968) Convergence of Probability Measures. John Wiley and Sons, New York.Google Scholar
[2] CraméR, H. (1955) Collective risk theory. Jubilee Volume of Försäkringsaktiebolaget Skandia. Nordiska Bokhandeln, Stockholm, 1–92.Google Scholar
[3] Darling, D. and Siegert, A. (1953) The first passage time problem for a continuous Markov process. Ann. Math. Statist. 24, 624–639.Google Scholar
[4] Liggett, T. and RoséN, B. (1968) A note on the correspondence between weak convergence in the function spaces C[0, 1] and D[0,1]. To appear.Google Scholar
[5] Prohorov, Yu. V. (1956) Convergence of random processes and limit theorems in probability theory. Theor. Probability Appl. 1, 157–214. (English translation.).CrossRefGoogle Scholar
[6] Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. John Wiley and Sons, New York.Google Scholar
[7] Skorohod, A. (1956) Limit theorems for stochastic processes. Theor. Probability Appl. 1, 262–290. (English translation.).Google Scholar
[8] Stone, C. (1963) Weak convergence of stochastic processes defined on semi-infinite time intervals. Proc. Amer. Math. Soc. 14, 694–696.Google Scholar