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Taking mortality distribution, surrender value, and tax relief factors into consideration, the authors construct an actuarial model for the influence of personal income tax deferred commercial pension insurance on changes in personal pension wealth and adopts a numerical simulation to deliver the corresponding changes in personal pension wealth to different initial insured age and different initial insured annual salary. In order to better measure the security level of the commercial pension insurance, the model for the net replacement rate of pension of the commercial pension insurance was further constructed. The results show that the effect of participating in the personal income tax deferred commercial pension insurance on the present value of personal pension wealth depends on the combined action of the initial insured age and the initial annual salary. Under the same insured age, because men retire later and work longer than women, men can obtain a higher accumulation of personal pension wealth than women. For insured persons with different income levels, high-income groups can obtain higher personal pension wealth growth, and although low-income groups cannot obtain higher personal pension wealth growth, they can obtain a significant increase in the pension replacement rate by participating in the insurance, thereby better guaranteeing their living standards after retirement. Regardless of the income level, tax relief can be obtained once participating in the insurance, but the value may vary. The optimal tax-saving age for men is 23 years old, and for women 25 years old. [ABSTRACT FROM AUTHOR]

In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount are exponentially distributed, respectively. Numerical examples are also given to further analyze the influence of relevant parameters on the actuarial function of the risk model. [ABSTRACT FROM AUTHOR]

Recently, the valuation of variable annuity products has become a hot topic in actuarial science. In this paper, we use the Fourier cosine series expansion (COS) method to value the guaranteed minimum death benefit (GMDB) products. We first express the value of GMDB by the discounted density function approach, then we use the COS method to approximate the valuation Equations. When the distribution of the time-until-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential Lévy process, explicit equations for the cosine coefficients are given. Some numerical experiments are also made to illustrate the efficiency of our method. [ABSTRACT FROM AUTHOR]