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Optimal reinsurance

Published online by Cambridge University Press:  14 July 2016

P. W. A. Dayananda
P. W. A. Dayananda*
Affiliation:
University of Ceylon, Colombo
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Extract

The fundamental principle underlying insurance is that the expected value of claims is equal to the premium. This was established by Bernoulli [4] in 1738. Subsequent work on the development of ‘risk theory’ led to research concerning the probability of ‘ruin’ of an insurance company. A critical study of these investigations was made by Borch [3] in a recent paper.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 1 , April 1970 , pp. 134 - 156
Copyright
Copyright © Applied Probability Trust 

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References

[1] Bather, J. A. (1963) Optimal regulation of a dam in continuous time. J. Soc. Appl. Math. 2, 33–63.Google Scholar
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[3] Borch, K. (1967) The theory of risk. J. R. Statist. Soc. B 29, 432–468.Google Scholar
[4] Bernoulli, D. (1738) Specimen theoriae novae de mensura sorits. Econometrica 2, 23–36. (English translation).Google Scholar
[5] Bellman, R. (1957) Dynamic Programming. Princeton University Press, Princeton.Google Scholar
[6] CraméR, H. (1930) On the mathematical theory of risk. Skandia Jubilee Volume, Stockholm.Google Scholar
[7] Dayananda, P. W. A. (1968) Optimal Control of Insurance. Ph.D. Thesis, University of Manchester.Google Scholar
[8] Lundberg, F. (1909) Über die Theorie der Rückversicherung. Trans. VI. Int. Cong. Actuaries 1, 877–955.Google Scholar