Bayesian Methods in Insurance Loss Modelling: Application to Nigerian Fire Claims Data

This study applies Bayesian statistical methods to insurance loss modelling using Nigerian fire insurance claims data, demonstrating the advantages of Bayesian inference over classical frequentist approaches in the context of limited and heterogeneous data. Bayesian methods allow the formal incorporation of prior information, update beliefs coherently as new data arrive, and naturally quantify parameter uncertainty, making them particularly valuable in insurance contexts where historical data are sparse or unreliable. This study uses fire insurance claims data from six non-life insurers in Lagos, Abuja, and Kano for the period 2016 to 2023, supplemented by international fire claims data used as informative priors. Bayesian hierarchical models are applied to estimate claim frequency and severity parameters by risk class and geographic zone, with Markov Chain Monte Carlo sampling implemented in Stan. Predictive posterior distributions for aggregate annual losses are compared against frequentist counterparts. Findings reveal that Bayesian hierarchical models produce significantly more stable and reliable parameter estimates than maximum likelihood estimation for subgroups with limited data, such as industrial fire risks in northern states where claims history is sparse. Predictive intervals from Bayesian models are appropriately wider, reflecting genuine parameter uncertainty. The study concludes that Bayesian methods offer a material improvement in fire insurance loss modelling reliability for the Nigerian market. It recommends that NAICOM encourage adoption of Bayesian actuarial methods through technical guidance publications.

Keywords: Bayesian methods, loss modelling, fire insurance, MCMC, actuarial statistics.