Applications of financial mathematics and statistical modeling in portfolio risk management
Yao Zhang
City University of Hong Kong
DOI: https://doi.org/10.59429/bam.v7i4.12404
Keywords: financial mathematics; portfolio risk management; modern portfolio theory; value-at-risk (VaR); statistical modeling
Abstract
Financial mathematics and statistical modeling have become fundamental tools in modern investment and risk management. As global financial markets show increasing complexity and volatility, mathematical modeling provides investors and institutions with systematic methods to quantify uncertainty, evaluate return expectations, optimize resource allocation, and control exposure to losses. This paper explores how financial mathematical theory—Including expected return modeling, variance–Covariance analysis, portfolio diversification theory, Value-at-Risk (VaR), and return forecasting using statistical regression—Supports investment decision-making and portfolio optimization. Using simulated daily portfolio return data generated from a stochastic normal distribution process, cumulative returns over a 100-day period are calculated and visualized. The results demonstrate that quantitative modeling helps investors measure volatility, balance return against risk, reduce uncertainty through diversification, and apply predictive analytics to forecast behavior under uncertain market conditions. The study reinforces that rigorous mathematical analysis is not only an academic discipline but also a practical requirement in real-world portfolio management and financial regulation.
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