Applied Mathematics in the Construction of Quantitative Investment Strategies and Risk Assessment

The integration of applied mathematics into quantitative finance has enabled systematic portfolio construction and rigorous risk assessment, yet most traditional approaches overly rely on variance as a risk proxy and fail to capture asymmetric and tail-dependent dynamics. Despite significant advances in stochastic modeling and portfolio optimization, there remains insufficient unification between mathematical modeling, coherent risk measures, and empirical investment practices. To address this gap, this study develops a comprehensive framework for quantitative investment that combines stochastic processes, convex and robust optimization, and risk-adjusted evaluation using Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), while conducting comparative experiments and analyses of naïve allocation, mean-variance optimization, and CVaR-adjusted models through case studies and simulations. The empirical results demonstrate that CVaR-based strategies outperform traditional mean-variance portfolios by achieving higher cumulative returns with superior downside protection, while robust optimization reduces drawdowns under market stress. This research advances the theoretical link between risk modeling and portfolio design and provides practical insights for institutional investors seeking resilient, mathematically grounded strategies in increasingly volatile financial markets.