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In order to alleviate the pressure of the basic endowment insurance system, China has implemented the policy of individual income tax-deferred commercial endowment insurance (IITDCEI) and actively explored the development path of individual supplementary endowment insurance. At present, the same tax rules are adopted for different income groups. Considering that people's income gap is large, different income groups enjoy different degrees of tax preference under this policy, which may cause social injustice and increase the gap between the rich and the poor. Based on this, we propose a new optimization scheme by adjusting the tax rate and the maximum premium limit of the insurance amount so as to coordinate the interests of low-, medium-, and high-income subjects and balance the degree of tax preference among the three subjects. At the same time, we also change the two parameters of the predetermined interest rate and retirement age, and compare the changes of the tax preference under the old and new schemes, and provide corresponding countermeasures for the implementation of the IITDCEI policy. [ABSTRACT FROM AUTHOR]

In this paper, we consider the compound Poisson risk model with stochastic premium income. We propose a new estimation of Gerber-Shiu function by an efficient method: Fourier-cosine series expansion. We show that the estimator is easily computed and has a fast convergence rate. Some simulation examples are illustrated to show that the estimation has a good performance when the sample size is finite. [ABSTRACT FROM AUTHOR]

This paper studies the statistical estimation of the Gerber-Shiu discounted penalty functions in a general spectrally negative Lévy risk model. Suppose that the claims process and the surplus process can be observed at a sequence of discrete time points. Using the observed data, the Gerber-Shiu functions are estimated by the Laguerre series expansion method. Consistent properties are studied under the large sample setting, and simulation results are also presented when the sample size is finite. [ABSTRACT FROM AUTHOR]