The flexible retirement system is one of the options of society endowment insurance system to deal with the aging. Therefore, the pension annuity under the system has important impact on theory and practice. This paper investigates the actuarial function of retirement annuity under the flexible retirement system. Under the hypothesis that the distribution of the retirement age is binomial distribution, the interest rate is decided by the discontinuous stochastic differential equations with jumps, and the death intensity is decided by Feller process with a jump. The formulas of the retirement annuity are proposed, including the life annuities, insurance, net premiums and insurance actuarial present value of second moment, and the simulatived estimation for the relevant actuarial functions is derived. These formulas provide the basis of the actuarial analysis of insurance and balance insurance under the flexible retirement system, thus they can be applied for the old-age insurance system and control of risk pension account in China.