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.

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.

This paper develops a multidimensional poverty index (MPI) evaluation system using multiple measures. We use the China Family Panel Study (CFPS) data to build balanced panel data from 2012 to 2018. Employing the probit model to analyze the impact of land transfer on relative poverty incidence, as well as utilizing the two-way fixed effects model and the logit model, we approach the issue from the perspective of multidimensional relative poverty identification. Our study indicates a decrease in relative poverty among rural households since 2012. Nonetheless, the overall incidence of relative poverty among rural households in China remains high at 20.6%, highlighting the severity of this issue in rural China. Moreover, we examine the heterogeneity of the poverty reduction effects of land transfer-in and land transfer-out. Land transfer can significantly reduce the incidence of relative poverty among rural households, with distinct mechanisms for land transfer-in and land transfer-out. Land transfer-in primarily reduces the relative poverty incidence of rural households through the education, housing, and land dimensions, while land transfer-out focuses on the quality-of-life dimension. Overall, land transfer-out has a more significant poverty reduction effect than land transfer-in. Furthermore, our study reveals that the reduction effect of land transfer on the incidence of relative poverty among rural households persists for at least two years, but by the fourth year, this effect disappears.

This paper incorporates time resource spent on caregiving, economic resource spent on caregiving, and delayed retirement into an overlapping generations (OLG) model to examine how delayed retirement affects the birth rate and through which pathways. It further measures and analyzes the impact of delayed retirement on the proportion of economic resource spent on caregiving relative to the total economic cost of raising children, as well as the joint effects on social welfare. The findings show that delayed retirement leads to a decline in the birth rate. Although it increases older participation in economic resource spent on caregiving, the positive effect of raising its proportion in the total cost of childrearing is outweighed by the negative effect of reduced time resource spent on caregiving. Numerical simulations reveal a reverse relationship between time resource spent on caregiving and economic resource spent on caregiving under the maximization of social welfare. Delayed retirement increases older participation in economic resource spent on caregiving and improves social welfare to some extent. Overall, social welfare rises because the positive effect of increased economic support outweighs the negative effect associated with delayed retirement. Therefore, it is necessary to promote the gradual implementation of delayed retirement and complement it with measures that reduce the time cost of childrearing for young parents so as to support higher fertility.

The contemporary era is defined by the rapid advancement of digital intelligence, a transformative force reshaping the landscape of higher education. Ideological and Political (I&P) courses in China, as a crucial component of cultivating socialist builders and successors, face both unprecedented opportunities and significant challenges in this new context. The traditional, one-way model of teaching, characterized by teacher-centered instruction and student passivity, is proving increasingly ineffective in engaging the digital-native generation. This paper posits that the "digital intelligence empowerment" paradigm offers a fundamental solution to the optimization of I&P course classroom interaction. Through a systematic analysis, this study first deconstructs the current dilemmas in I&P course interaction, identifying generational, institutional, and pedagogical barriers. Subsequently, it explores the multi-faceted ways in which digital intelligence technologies—such as big data analytics, artificial intelligence (AI), and extended reality (XR)—can empower this interactive process. The core of this paper proposes a "Three-Dimensional Empowerment Model" for optimizing classroom interaction, focusing on intelligent infrastructure, pedagogical innovation, and institutional support. It details three critical implementation paths: creating an immersive interactive atmosphere through XR to foster emotional resonance; fostering collaborative learning using AI-driven platforms; and achieving personalized guidance through big data analytics. Finally, the study outlines corresponding countermeasures, including strengthening teacher digital literacy and ensuring ethical data use, to ensure the successful implementation of these paths. The ultimate goal is to transform I&P course classrooms into dynamic ecosystems of critical thinking and deep-seated value internalization.