The aggregate claims distribution of a life insurance portfolio with a pairwise positive dependence structure
The individual life model has always been considered as the one closest to the real situation of the total claims of a life insurance portfolio. It only makes the nearly inevitable assumption of independence of the lifelenghts of insured persons in the portfolio. Many clinical studies, however, have demonstrated positive dependence of paired lives such as husband and wife. In our opinion, it wont be unrealistic expecting a considerable number of married couples in any life insurance portfolio (e.g. life insurance contracts formalized at the time of signing a mortatge) and these dependences materially increase the values for the stop-loss premiums associated to the aggregate claims of the portfolio. Since the stop-loss order is the order followed by any risk averse decison maker, the simplifying hypothesis of independence constitute a real financial danger for the company, in the sense that most of their decisions are based on the aggregated claims distribution. In this paper, we will determine approximations for the distribution of the aggregate claims of a life insurance portfolio with some married couples and we will describe how to make safe decisions when we dont know exactly the dependence structure between the risks in each couple. Results in this paper are partly based on results in Dhaene and Goovaerts (1997).
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- Denuit, M., 2000. "Stochastic Analysis of Duplicates in Life Insurance Portfolios," Papers 0004, Catholique de Louvain - Institut de statistique.
- Dhaene, J. & Goovaerts, M. J., 1997. "On the dependency of risks in the individual life model," Insurance: Mathematics and Economics, Elsevier, vol. 19(3), pages 243-253, May.
- Denuit, M., 2000. "Stochastic Analysis of Duplicates in Life Insurance Portfolios," Papers 4, Catholique de Louvain - Institut de statistique.
- Hu, Taizhong & Wu, Zhiqiang, 1999. "On dependence of risks and stop-loss premiums," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 323-332, May.
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