Stochastic Modelling of Claim Arrival Processes in Nigerian Non-Life Insurance Companies

This study applies stochastic modelling techniques to analyze claim arrival processes in Nigerian non-life insurance companies, with the aim of improving reserve estimation and solvency management. Accurate modelling of claim frequency and timing is a foundational actuarial task that underpins reserve adequacy, product pricing, and capital requirement calculations. Traditional deterministic reserving methods used by many Nigerian insurers may inadequately capture the randomness inherent in claim arrival patterns, particularly in high-severity low-frequency lines such as fire and engineering insurance. This study uses historical claims data obtained from five non-life insurers operating in Lagos, Port Harcourt, and Kano for the period 2018 to 2023. Poisson, negative binomial, and mixed Poisson models are fitted to observed claim count distributions for motor, fire, and marine insurance lines. Goodness-of-fit tests including Kolmogorov-Smirnov and chi-square tests are applied to identify the best-fitting model for each line. Findings reveal that claim arrivals in motor insurance are well described by a negative binomial process, while fire insurance claims exhibit overdispersion consistent with a mixed Poisson model. Standard Poisson assumptions underestimate claim volatility in all lines examined. The study concludes that stochastic claim arrival models provide superior reserve and solvency estimates compared to deterministic methods for Nigerian non-life insurers. It recommends that NAICOM incorporate minimum stochastic modelling standards into its risk-based supervision framework.

Keywords: stochastic modelling, claim frequency, non-life insurance, reserve estimation, Poisson process.