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


62P05 Applications of statistics to actuarial sciences and financial mathematics
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[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 Chicago, IL
[3] Carter, R.L., Reinsurance, (1979), Kluwer London
[4] Centeno, L., On combining quota-share and excess of loss, Astin bulletin, 15, 49-63, (1985)
[5] Gerber, H.U., An introduction to mathematical risk theory, (1979), Irwin Homewood, IL · Zbl 0431.62066
[6] Panjer, H.H., Direct calculation of ruin probabilities, (1983), University of Waterloo Waterloo · Zbl 0521.62082
[7] Van Wouwe, M.; De Vylder, F.; Goovaerts, M., The influence of reinsurance limits on infinite time ruin probabilities. premium calculation in insurance, NATO ASI series, (1984) · Zbl 0539.62112
[8] Waters, H.R., Excess of loss reinsurance limits, Scandinavian actuarial journal, 37-43, (1979) · Zbl 0399.62106
[9] Waters, H.R., Some mathematical aspects of reinsurance, Insurance: mathematics and economics, 2, 17-26, (1983) · Zbl 0505.62085
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