This paper explores how the medical expenditure risk affects the households’ portfolio choice across health status theoretically in a life cycle model and empirically using machine learning methods. Medical expenditure risk, as a background risk, has the potential to influence households’ financial decisions. A higher medical expenditure risk leads to a larger fluctuation and more uncertainty in households’ consumption and therefore utility. As a result, risk-free assets become more attractive. Our machine learning analysis provides evidence that aligns with the predictions of the theoretical life cycle model. Specifically, households with better health hold a larger proportion of stocks in their portfolios. Furthermore, when facing increased medical expenditure risk, households in good health demonstrate a greater willingness to invest in safe assets.

Population, as a fundamental element in urban development, often reflects a city's economic development pattern through its spatial distribution and dynamic changes. Studying population spatial distribution is pivotal for bolstering the economic activity capacity in urban agglomerations and guiding regional economic health. Using the Changsha-Zhuzhou-Xiangtan urban agglomeration as a case study, this paper analyzes its overall spatial structure and the spatiotemporal evolution of population at the district and county levels. This analysis utilizes population density, population redistribution index, and population geographic concentration as key indices. Additionally, a spatial econometric model is constructed to assess the impact of economic, social, and environmental factors on population spatial patterns. Findings reveal several key points: (1) Furong District serves as the primary central area, boasting a population geographic concentration of 25.1% in 2021. Tianxin District, Kaifu District, Yuhua District, Shifeng District, Yuelu District, and Hetang District constitute the secondary central areas, while Yutang District, Tianyuan District, Lusong District, Yuhu District, Wangcheng District, and Changsha County form the tertiary level areas. (2) Population density within the Changsha-Zhuzhou-Xiangtan urban agglomeration gradually decreases from Furong District outward. The first central area and sub-central areas experience increasing population density, highlighting a polarization trend in the population distribution. (3) The overall Moran's index for the spatial distribution of population in the Changsha-Zhuzhou-Xiangtan urban agglomeration is significantly positive, indicating a strong spatial autocorrelation and a deepening spatial agglomeration of population distribution. (4) Per capita disposable income, financial expenditure, and education level positively influence the geographical concentration of population in the urban agglomeration, while GDP per capita, road area per capita, and environmental quality exert a negative impact. Notably, the most influential factors shaping population spatial distribution are GDP per capita, disposable income per capita, and air quality.