Sustainable development has become an important global goal for environmental protection and economic growth. Promoting environmental sustainability and green development has become an inevitable trend for global economic transformation. The carbon emission trading market (carbon market) is a crucial market-based mechanism for pricing greenhouse gas emissions, where carbon trading prices signal the costs of emission reduction and drive firms to engage in green technology innovation for a low-carbon transition. Using a sample of A-share listed companies in China’s eight carbon pilot regions from 2013 to 2024, this study employs a two-way fixed effects model to examine how carbon prices affect both the quantity and quality of corporate green technological innovation. Baseline regressions show that a one-unit increase in carbon prices significantly boosts green patent quantity (GreNum) by 0.018 and quality (GreQua) by 0.361, both at the 1% significance level. Mechanism analysis reveals that financing constraints act as a partial mediator, while environmental regulation and media attention further amplify the positive impact of carbon prices on corporate green technological innovation. Heterogeneity analysis further indicates that this positive effect is more pronounced in non-high-tech enterprises, China’s northern and eastern regions, and state-owned enterprises. This study provides empirical evidence for optimizing carbon market allocation, supporting corporate low-carbon transition, and promoting global environmental sustainability and green development.

During the process of portfolio decision, the investor usually assumes that the distribution of asset return is known in order to identify the optimal investment strategy. In fact, the distribution of asset return is unknown and the investor often uses the historical data to estimate its distribution, which is uncertainty and should be taken into account during the process of portfolio decision. In this paper, we use the relative entropy to measure the uncertainty degree of risk premia and covariance matrix, build the model of mean-variance portfolio, and obtain the portfolio’s risk premia and variance under the worst scenario. At last, a comparative empirical study based on the portfolio’s effective frontier is performed. Results show: parameter uncertainty has significant effect on portfolio decision, and the effect of risk premium uncertainty is more than that of covariance matrix uncertainty; for the investor of risk-aversion, the higher the degree of parameter uncertainty is, the lower the portfolio performance is, and the stronger the relationship of assets in portfolio is, the weaker the effect of parameter uncertainty on portfolio is.