As health insurance markets become increasingly complex due to demographic shifts, cost volatility, and regulatory reforms, accurately evaluating actuarial risk is essential for sustainable portfolio management. Traditional risk models often fall short in capturing nonlinear dependencies, tail co-movements, and dynamic uncertainty inherent in multi-claim health insurance portfolios. This study introduces a hybrid framework that combines copula-based multivariate time series modeling with Bayesian statistical learning to enhance the precision and interpretability of actuarial risk assessment in health insurance portfolios. From a broader perspective, we address systemic risk aggregation and marginal risk attribution by modeling the joint distribution of key health insurance variables such as claim frequency, severity, premium income, and policyholder lapse rates using copulas that preserve dependence structures beyond simple correlation metrics. This is particularly effective in stress scenarios where tail dependencies become pronounced. The time-varying copula approach allows us to dynamically capture changing dependence over time, especially during economic cycles or epidemiological events. Bayesian learning methods are employed to estimate posterior distributions of key parameters, enabling the integration of prior actuarial expertise with observed data. This probabilistic inference allows for more robust risk prediction, especially when dealing with sparse or heterogeneous datasets. We demonstrate the model's performance using a real-world dataset from a regional health insurance provider, focusing on tail risk prediction, reserve adequacy, and portfolio solvency under multiple stress scenarios. The results show that the proposed copula-Bayesian framework significantly outperforms classical GLM-based models in capturing extreme joint outcomes and predicting future liabilities. This integrated approach provides actuaries and portfolio managers with a more resilient decision-support tool for pricing, reserving, and capital allocation in volatile health insurance environments.