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Measuring the effects of reinsurance by the adjustment coefficient. (English) Zbl 0598.62141

The author determines under certain conditions optimal forms of reinsurance which are combinations of quota-share and excess of loss treaties. With regard to Lundberg’s inequality he uses maximizing of the adjustment coefficient as the optimality criterion. For the determination of the solution it is assumed that the aggregate claims are compound Poisson distributed, that the reinsurance premium for the quota-share is proportional to the original premium and the excess of loss premium is calculated according to the expected value principle. Some numerical examples illustrate the results.
Reviewer: A.Reich

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
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References:

[1] Andreadakis, M.; Waters, H. R., The effect of reinsurance on the degree of a risk associated with an insurer’s portfolio, Astin Bulletin, 11, 119-135 (1980)
[2] Bowers, N. L.; Gerber, H. U.; Hickman, J. C.; Jones, D. A.; Nesbit, C. J., Society of Actuaries study note on risk theory (1982), Society of Actuaries: Society of Actuaries Chicago, IL
[3] Carter, R. L., Reinsurance (1979), Kluwer: Kluwer London
[4] Centeno, L., On combining quota-share and excess of loss, Astin Bulletin, 15, 49-63 (1985)
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