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de Lourdes Centeno, Maria

Excess of loss reinsurance and Gerber’s inequality in the Sparre Andersen model. (Excess of loss reinsurance and Gerber’s inequality in the Sparre Anderson model.) (English) Zbl 1074.91567

Insur. Math. Econ. 31, No. 3, 415-427 (2002).
Summary: Assuming that the reinsurance premium is calculated according to the expected value principle we study an upper bound for the probability of ruin in finite horizon, as function of the excess of loss retention limit. The upper bound used is an extension proved by J. Grandell [Aspects of Risk Theory. New York: Springer (1991; Zbl 0717.62100)] of Gerber’s bound, see [H. U. Gerber, Mitt. Verein. Schweiz. Versicherungsmath. 73, 205–216 (1973; Zbl 0278.60047)], for the Sparre Andersen model [“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)].

Cited in 11 Documents

MSC:

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

Keywords:

Sparre Andersen model; reinsurance; excess of loss; adjustment coefficient

Citations:

Zbl 0717.62100; Zbl 0278.60047
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\textit{M. de Lourdes Centeno}, Insur. Math. Econ. 31, No. 3, 415--427 (2002; Zbl 1074.91567)
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References:

[1] Centeno, M.L., Measuring the effects of reinsurance by the adjustment coefficient, Insurance: mathematics and economics, 5, 169-182, (1986) · Zbl 0598.62141
[2] Centeno, M.L., 1997. Excess of loss reinsurance and the probability of ruin in finite horizon. ASTIN Bulletin 27, 59-70.
[3] Centeno, M.L., 2002. Measuring the effects of reinsurance by the adjustment coefficient in the Sparre Anderson model. Insurance: Mathematics and Economics 30, 37-49. · Zbl 1037.62106
[4] Gerber, H.U., 1973. Martingales in risk theory. Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, pp. 205-216. · Zbl 0278.60047
[5] Gerber, H.U., 1979. An Introduction to Mathematical Risk Theory, S.S. Huebner Foundation Monographs. University of Pennsylvania. · Zbl 0431.62066
[6] Grandell, J., 1991. Aspects of Risk Theory. Springer, New York. · Zbl 0717.62100
[7] Sparre Anderson, E., 1957. 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.
[8] Waters, H., Some mathematical aspects of reinsurance, Insurance: mathematics and economics, 2, 17-26, (1983) · Zbl 0505.62085
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