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Centeno, Maria de Lourdes

Measuring the effects of reinsurance by the adjustment coefficient in the Sparre Andersen model. (Measuring the effects of reinsurance by the adjustment coefficient in the Sparre Anderson model.) (English) Zbl 1037.62106

Insur. Math. Econ. 30, No. 1, 37-49 (2002).
Summary: We study the insurer’s adjustment coefficient as a function of retention levels for combinations of quota-share with excess of loss reinsurance in the Sparre Andersen model [E. Sparre Andersen, “On the collective theory of risk in the case of contagious between the claims”, in: Proceedings of the Transactions on XV International Congress of Actuaries, New York (1957)]. We show that the insurer’s adjustment coefficient is a unimodal function of the retention levels when the quota-share reinsurance premium is calculated on original terms and when the excess of loss premium is calculated according to the expected value principle.

Cited in 10 Documents

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)

Keywords:

Sparre Andersen model; adjustment coefficient; reinsurance; excess of loss; quota-share; combinations of excess of loss and quota-share reinsurance
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\textit{M. de L. Centeno}, Insur. Math. Econ. 30, No. 1, 37--49 (2002; Zbl 1037.62106)
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References:

[1] Carter, R.L., 1979. Reinsurance. Kluwer Academic Publishers, Dordrecht, in association with the Mercantile and General Reinsurance Co., London.
[2] Centeno, M.L., On combining quota-share and excess of loss, ASTIN bulletin, 15, 49-63, (1985)
[3] Centeno, M.L., Measuring the effects of reinsurance by the adjustment coefficient, Insurance: mathematics and economics, 5, 169-182, (1986) · Zbl 0598.62141
[4] Gerber, H.U., 1979. An Introduction to Mathematical Risk Theory. S.S. Huebner Foundation Monographs, University of Pennsylvania. · Zbl 0431.62066
[5] Grandell, J., 1991. Aspects of Risk Theory. Springer, New York. · Zbl 0717.62100
[6] Hesselager, O., 1990. Some results on optimal reinsurance in terms of the adjustment coefficient. Scandinavian Actuarial Journal 1-2, 80-95. · Zbl 0728.62100
[7] Sparre Anderson, E., 1957. On the collective theory of risk in the case of contagious between the claims. In: Transactions of the XV International Congress of Actuaries.
[8] Waters, H., 1979. Excess of loss reinsurance limits. Scandinavian Actuarial Journal 1, 37-43. · Zbl 0399.62106
[9] Waters, H., Some mathematical aspects of reinsurance, Insurance: mathematics and economics, 2, 17-26, (1983) · Zbl 0505.62085
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