This dissertation comprises three essays that advance the theory and application of risk modeling in financial and actuarial domains. The first chapter introduces the overarching motivation, research themes, and methodological orientation of the dissertation. Particular emphasis is placed on the development of robust statistical tools to address key challenges in empirical finance and insurance risk management, including structural breaks, tail risk, volatility clustering, risk forecasting, and optimal risk-sharing. The second chapter develops a new, distribution-free test for financial contagion, aimed at detecting structural breaks in residual dependence between asset returns during crisis periods. Unlike traditional contagion tests that rely on strong parametric assumptions, the proposed method accommodates heteroscedasticity through a deterministic volatility jump model and leverages block-based variance estimators for valid inference. The resulting test remains robust under time-varying volatility and dependent innovations and outperforms classical benchmarks in both size control and power across a range of simulated and historical crisis episodes, including the COVID-19 and subprime mortgage crises. Chapter 3 addresses the optimal reinsurance retention problem under regulatory frameworks that use Value-at-Risk (VaR) and Expected Shortfall (ES) as capital standards. It revisits the performance and limitations of the traditional stop-loss (SL) contract, demonstrating that SL-optimal solutions under VaR imply unrealistic outcomes such as zero insolvency probability. A generalizable framework is developed using Excess-of-Loss (EoL) reinsurance, where optimal retention is characterized via central limit approximations and distortion risk measures. The framework admits several premium loading principles, including standard deviation and Sharpe ratio principles, and allows for tractable, asymptotically valid estimation procedures. The last chapter proposes a simulation-consistent and distributionally robust method for multi-horizon Value-at-Risk forecasting under ARMA-GARCH models. The approach estimates the gamma-quantile of the maximum return over a fixed horizon. Parameters are estimated via weighted quasi-maximum likelihood, and uncertainty is quantified using a residual-based bootstrap. The methodology is validated through simulation and applied to ten years of asset-level financial returns. Together, these essays contribute new tools and perspectives to the literature on financial contagion, reinsurance optimization, and tail risk forecasting.