Application and Challenges of Mathematical Modeling in Financial Market Risk Assessment

This study discusses in detail the core application of mathematical modeling in financial market risk assessment, emphasizing the importance of modeling in identifying and quantifying market, credit and operational risks. The article first introduces the basic process of mathematical modeling, including model construction, verification, and the important steps of selecting appropriate mathematical tools to describe financial risks. We comprehensively examine a variety of mathematical models, such as stochastic processes, time series analysis, and machine learning techniques, and discuss their applicability and limitations in risk assessment. In particular, this article demonstrates how to estimate the potential maximum loss of an asset by introducing a value-at-risk (VaR) model, and uses a logistic regression model to predict the probability of default. The research shows how to apply these models to large-scale financial data and how to visually present the model results in the form of charts. Finally, the article emphasizes that risk assessment is a dynamic process that must be constantly updated and adjusted as market conditions change.