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**Insurance contracts portfolios with heterogeneous parametric life distributions.**
*(English)*
Zbl 1144.91024

This paper is a further development of the authors’ previous work [Scand. Actuar. J. 2002, No. 3, 212–222 (2002; Zbl 1039.91037); Insur. Math. Econ. 33, No. 3, 567–584 (2003; Zbl 1103.91360)] focused on the effect of the stochastic heterogeneity of insurance contracts. In the present paper two portfolios are considered: one of \(m\) endowment insurance contacts and other one of \(m\) whole life insurance contracts. The authors assumed that the owners of the portfolios are exposed to different members of a known parametric family of distributions and studied the impact of such heterogeneity on the annual premiums and death benefits. For this purpose they discussed the notions of the majorization order, Schur functions and introduced the convenient parametric families of distribution functions, discussed their properties, proved that premiums paid in both contracts are Schur concave, while the death benefit awarded in the whole life contract is Schur convex, obtained upper and lower bounds for the premiums and for the death benefit. Numerical examples for exponential, Gompertz, Weibull and Pareto life-distributions are discussed.

Reviewer: N. M. Zinchenko (Kyïv)

### MSC:

91B30 | Risk theory, insurance (MSC2010) |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

### Keywords:

endowment insurance; whole life insurance; force of mortality; distribution function; Schur convex and concave functions; annual premium, death benefit
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\textit{M. Dahan} et al., Scand. Actuar. J. 2004, No. 6, 431--447 (2004; Zbl 1144.91024)

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### References:

[1] | Arnold BC, Lecture Notes in Statistics (1987) |

[2] | Bowers NL, Actuarial Mathematics (1986) |

[3] | DOI: 10.1080/034612302320179872 · Zbl 1039.91037 |

[4] | DOI: 10.1016/j.insmatheco.2003.08.001 · Zbl 1103.91360 |

[5] | Jones BL Mereu JA (2000)A family of fractional age assumptions27 |

[6] | Jones BL Mereu JA (2002)A Critique of fractional age assumptionsInsuranceMathematics and Economics30 |

[7] | Jordan CW, Life Contingencies (1975) |

[8] | Marshall AW, Inequalities: theory of majorization and its applications (1979) · Zbl 0437.26007 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.