Financial Mathematics in Risk Management: Construction and Optimization of Quantitative Models

In today's era of continuous evolution and increasing complexity within financial markets, risk management has emerged as one of the most crucial issues in the realm of finance. As an interdisciplinary subject that artfully integrates mathematics, statistics, and finance, financial mathematics offers powerful quantitative tools for effective risk management. This paper undertakes an in-depth exploration of financial mathematics in the context of risk management. It introduces the construction methods of various quantitative models, such as the Value at Risk (VaR) model and the Conditional Value at Risk (CVaR) model. Through the utilization of actual data, a comprehensive application analysis of these models is conducted. Simultaneously, the paper delves into the optimization of quantitative models, proposing improved methods and strategies. To enhance the visual understanding, the article incorporates two pictures and two tables to vividly display the construction process and results of the model. This provides a highly useful reference for financial institutions and investors in their pursuit of effective risk management strategies.