Actuarial present values in continuous annuities based on Hossian Assumption

Continuous life annuities have an important role in life insurers, and it is necessary to utilize a fractional age assumption when we calculate the actuarial present values of these life annuities. Obviously, the rationality of the assumption decides the calculation accuracy. Comparing with other used assumptions, the death information of the life table can be utilized more adequately under this assumption. At the same time, we can obtain the continuous mortality force in all life time if this assumption is used, and this assumption also has other good geometric properties. Hence, Hossion Assumption can improve the estimated accuracy of fractional age mortality rates. Based on Hossian Assumption, the actuarial present values (abbreviated to APVs) of three continuous life annuities are discussed. We obtain the calculation expressions of these APVs based on Hossian Assumption. In addition, using the experience life table of the Chinese Pension (2000-2003) (male), the numerical calculations are carried out respectively. And we compare the results with ones under UDD assumption.