Study On The Linear Increasing Payment Life Insurance With Random Interest Rate

Interest randomness in life insurance has been paid attention to in recent years onactuarial theory and its application, In this paper, n-year linear increasing payment life insurance with the stochastic interest with discrete and continuous condition was discussed. In discrete condition, considering two cases of independent identical distribution and dependent distribution, we gave the moment, the second moment and variance, In continuous condition, models of the random rate of interest were established respectively by Gauss process, Wiener process or O-U process. The moment , the second moment and variance of the payable present value under the three cases were given. Moreover, the special expression of the moment, the second moment and variance with De Moivre's death rate were given. Finally, considering abrupt event's effect on interest, we established the models of the random rate of interest jointly by Gauss process and Poisson process, Wiener process and Poisson process or O-U process and Poisson process, also gave the moment, the second moment and variance of the payable present value under the three cases. Moreover giving the special expression of the moment, the second moment and variance with De Moivre's death rate.