Two approximations of the present value distribution of a disability annuity
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摘要
The distribution function of the present value of a cash flow can be approximated by means of a distribution function of a random variable, which is also the present value of a sequence of payments, but with a simpler structure. The corresponding random variable has the same expectation as the random variable corresponding to the original distribution function and is a stochastic upper bound of convex order. A sharper upper bound can be obtained if more information about the risk is available. In this paper, it will be shown that such an approach can be adopted for disability annuities (also known as income protection policies) in a three state model under Markov assumptions. Benefits are payable during any spell of disability whilst premiums are only due whenever the insured is healthy. The quality of the two approximations is investigated by comparing the distributions obtained with the one derived from the algorithm presented in the paper by Hesselager and Norberg [Insurance Math. Econom. 18 (1996) 35–42].
论文关键词:Convex order,Comonotonic joint distribution,Multistate life insurance contracts,Present value distributions
论文评审过程:Received 24 November 2004, Revised 19 February 2005, Available online 10 May 2005.
论文官网地址:https://doi.org/10.1016/j.cam.2005.03.071