Regime-switching approaches for dynamic risk and dependence modeling of insurance claim frequency and severity

Abstract

This study advances dynamic risk and dependence modeling in general insurance by applying regime-switching approaches that aim to accurately capture nonlinear, asymmetric, time-varying structures and regime shifts in claim frequency and severity, limitations often overlooked by traditional methods such as Pearson correlation, static copulas, and single-regime models. The Local Gaussian Correlation (LGC) framework is used to analyze monthly and weekly insurance severity data from Kenya and Norway. By combining LGC with Hidden Markov Models (LGC-HMM), the study reveals time-varying dependencies across different lines of business. Diagnostic checks using Auto Correlation Functions (ACFs) confirm the validity of the framework. Furthermore, comparisons of Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) show that LGC-HMM models achieve higher accuracy and exhibit asymmetric diversification benefits. For Claim Frequency modeling, weekly motor insurance data from Uganda, covering periods before, during, and after COVID-19, are analyzed using the Regime-Switching Integer-Valued Generalized Autoregressive Conditional Heteroskedasticity (RS-INGARCH) framework, estimated via the Extended Hamilton-Gray algorithm. Among the lag options, RS-INGARCH(1,1) is chosen for its simplicity and effectiveness. A similar analysis with Kenyan motor insurance data enhances regional generalizability. Comparisons with INAR(1) and INGARCH models indicate that RS-INGARCH provides improved in-sample fitting and out-of-sample forecasting, supported by appropriate residual diagnostics using ACFs and Ljung-Box tests. The findings highlight the need for regime-switching models to manage volatility and structural changes in insurance claims. The LGC-HMM framework aids dependence analysis, while RS-INGARCH enhances claim frequency modeling. Together, these approaches offer insurers and regulators valuable tools for solvency monitoring and riskbased decision-making, especially in developing markets facing uncertainty from regulatory reforms and systemic shocks like the COVID-19 pandemic.