Model Of Life Actuarial On Credibility Space

The traditional models of life actuarial were founded on the probability space and based the real random variables. However, in the real world, the life insurance is often shown as the uncertainty of fuzzy. Credibility measure, a new method, to be describes the fuzziness. Based on this, this paper founded the models of life actuarial on the credibility space, thus extends the life actuarial theory from probability space to credibility space. Firstly, when the fuzzy variable takes value on interval, the credibility distribution expressions of the fuzzy variable are given, meanwhile, the conditional credibility distribution expressions of the fuzzy variable are presented when the fuzzy variable takes value in interval; Secondly, this paper proposed several concepts of life distribution function, survival distribution function and expectation of life, and discusses the expressions of the future lifetime and expectation of life on the credibility space; Furthermore, the actuarial present value models of the death insurance are founded on the credibility space; Finally, the actuarial present value models of several basic life annuities are founded on the credibility space.