Ruin Theory Applications to Solvency Risk Assessment in Small Nigerian Insurance Companies

This study applies classical and generalized ruin theory models to assess solvency risk in small Nigerian insurance companies, providing a theoretically rigorous framework for understanding the probability of insurer insolvency under realistic claims and premium income processes. Classical ruin theory, rooted in the Cramér-Lundberg model, offers closed-form and simulation-based tools for computing the probability of an insurer's surplus becoming negative over finite and infinite time horizons. This study adapts classical ruin theory to the Nigerian insurance context by calibrating claim frequency and severity parameters from the historical data of 15 small-to-medium non-life insurers operating in Anambra, Ogun, and Kano States for 2018 to 2023. Finite-time ruin probability curves are computed for each insurer at observed safety loading levels. Sensitivity analysis examines the impact of reinsurance, premium rate changes, and capital injections on ruin probability. Findings reveal that several small insurers operate with finite-time 10-year ruin probabilities exceeding 15 percent under their observed claims and premium income parameters, indicating materially inadequate safety margins. Reinsurance cession is shown to substantially reduce ruin probability for high-volatility portfolios. The study concludes that ruin theory provides practically useful solvency insights for small Nigerian insurers that complement ratio-based regulatory indicators. It recommends that NAICOM pilot ruin probability reporting as a supplementary supervisory tool for small and medium insurers.

Keywords: ruin theory, solvency risk, small insurers, Cramér-Lundberg, Nigeria.