In the context of the rapid development of big data technology, developing an artificial intelligence economy is beneficial to China’s economic transformation, industrial upgrading, and enhancing international competitiveness. This paper first constructs a financial mathematical model of the AI economy based on the theoretical foundation of financial mathematics. The structure of the financial mathematical model mainly consists of three parts: portfolio model, capital asset pricing model, and financial derivatives pricing model. To address the problem of the unstable development of China’s AI economy, the theoretical framework of investment risk management is constructed, which can help investors intelligently implement investment risk management plans and implement investment risk management countermeasures and measures. Finally, to verify the performance of the risk investment optimization model and intelligent algorithm proposed in this chapter, three investment scales will verify the investment risk management capability based on the portfolio model. The results show that the convergence performance of the portfolio model is 0.2025, 0.4021, and 0.4391 for three investment sizes of 2, 4, and 9, and the penalty coefficients are 1.5, 28, and 0.2, respectively. At the beginning of the iteration, the investment risk is high, and the convergence speed of the portfolio model is higher than the capital asset pricing model and the financial derivatives pricing model. This study applies it to solve financial optimization problems, including portfolio, stock forecasting, risk management, and many other fields, and provides a better solution to the optimization decision problem of the portfolio.