A life annuity is a series of payments made at fixed intervals while the annuitant is alive. It has been a major part of actuarial science for a long time and it plays an important role in life insurance operations. In order to explore the interaction of various risks in an annuity portfolio, we decompose the liabilities by using the so called Martingale Representation Theorem (MRT) decomposition. The MRT decomposition satisfies all 6 meaningful properties proposed by Schilling et al. (2015).

      Before presenting some numerical examples to illustrate its applicability, several stochastic mortality models are compared and the Renshaw–Haberman (RH) model is chosen as our projection model. Then we compare two one-factor short rate models and estimate the parameters of CIR model to construct the stochastic interest rate setting. Finally, we allocate risk capitals to risk factors obtained from the MRT decomposition according to the Euler principle and analyze them when the age of cohort and the deferred term change.