Author(s)

Yutong Yang

Corresponding Author

Yutong Yang

Abstract

Against the backdrop of intensified volatility in global capital markets, this study focuses on the application of financial mathematical models and statistical inference in portfolio optimization to address the imbalance between traditional empirical investment returns and risks. Firstly, this article provides a detailed overview of the basic frameworks of mean variance model, CAPM model, and APT model, analyzes these three types of models, and studies their quantitative roles in determining optimal asset allocation ratios, risk pricing guidance and portfolio adjustment, and multi factor perspective portfolio optimization; Furthermore, this article also elaborates that statistical inference provides reliable data support for model applications through parameter estimation, validity testing, and significance analysis, avoiding decision bias. Research has shown that combining the quantitative framework of financial mathematical models with the validation support of statistical inference can fundamentally enhance and improve the scientific and objective nature of investment decisions. However, it is still worth noting that the limitations of simplifying assumptions and historical data in this model must be recognized. This article hopes to optimize and improve the adaptability of the model through dynamic data updates in the future, so that the model can better adapt to complex markets.

Keywords

Financial mathematical models; Statistical inference; Portfolio optimization; Risk-reward trade-off