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**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

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.

### 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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