Description: This paper investigates the use of models of dependent mortality for determining annuity values. We discuss a broad class of parametric models using a bivariate survivorship function called a copula. Using data from a large insurance company to illustrate our methods, we calculate maximum likelihood estimates to calibrate the rnodel.

Description: We propose an age-shift model to modify the LC model and deal with the problem of parameters. The proposed method attains smaller estimation errors with respect to mean absolute percentage error or mean square error. We also apply the proposed age-shift model to the mortality rates of these four countries to evaluate the longevity risk in annuity products by measuring life expectancy.