Dependence modeling in general insurance using local Gaussian correlations and hidden Markov models

This article introduces a hybrid framework that combines local Gaussian correlation (LGC) with hidden Markov models (HMMs) to model dynamic and nonlinear dependencies in general insurance claims, thereby addressing the limitations of static copula methods. When applied to Kenyan motor insurance claims (2008–2021) and Norwegian home insurance data (2012–2018), the proposed LGC-HMM approach captures regime-specific, nonlinear dependency patterns, revealing distinct stable and crisis periods through structural breaks in the dependency structure. Diagnostic checks confirm the HMM’s ability to reduce residual serial dependence, validating the latent state dynamics. Regime-aware value-at-risk (VaR) and tail VaR estimates derived from the LGC-HMM, using a proposed simulation procedure, outperform static copula models by adapting to structural changes, demonstrating robust forecasting performance. Visualization of forecasts via LGC maps further illustrates evolving tail dependencies. These findings support improved risk diversification and crisis-sensitive pricing strategies in actuarial practice.