Approximations For Continuous Life Annuities In A Stochastic Financial Environment

In this paper, we mainly consider the distribution of a continuous life annuity when both the decrements and the interest rates are assumed to be stochastic. In order to analyze the continuous life annuity more accurate, we have no limi-tation in determining its order moments, and determine some sophisticated risk measures like Value-at-Risk or Tail Value-at-Risk. In this thesis, we propose to use the theory of comonotonic risks developed in Dhaene et al.(2002). This methology allows to obtain convex order bound of the continuous life annuity. Furthermore, we determine its local optimal lower bound under the principle of maximizing the first order Taylor expansion of the conditional variance. Finally, we obtain reliable approximations of risk measures of continuous life annuity, in particular very accurate estimates of upper quantiles and stop-loss premiums.