PERFORMANCE LOSS QUANTIFICATION IN KERNEL DENSITY ESTIMATION FOR ACTUARIAL AND FINANCIAL ANALYSIS
Abstract
Accurately estimating aggregate loss distributions is critical in actuarial and financial risk assessment, as it underpins effective risk analysis and the development of mitigation strategies. However, incorrect parametric assumptions can lead to biased risk estimates and underestimated losses. Non-parametric methods, such as Kernel Density Estimation (KDE), offer a flexible alternative by generating smooth empirical probability density functions (PDFs) directly from sample data without assuming a specific distributional form. This study examines the impact of dependence structures on risk measures by applying KDE with a Gaussian kernel to estimate aggregate loss distributions. To quantify the effects of ignoring dependence, we introduce the concept of performance loss, focusing on variance, Value at Risk (VaR), and Tail Value at Risk (TVaR). The results show that performance loss increases with the correlation coefficient, indicating that higher dependency leads to greater underestimation of risk. Additionally, higher confidence levels amplify performance loss for VaR and TVaR, underscoring the sensitivity of these measures to tail behavior. These findings highlight the importance of incorporating dependence structures in risk modeling to avoid misleading evaluations. The implications are particularly relevant for disaster risk management in Central Asia, where overlooking interdependencies in seismic losses could result in inadequate financial and actuarial strategies.
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