Tail Risk, Capital Adequacy, and Reinsurance Structure in Emerging Insurance Markets: A Pareto Type II Severity Modelling

Abstract

Actuarial pricing, solvency assessment, and capital determination in emerging insurance markets depend heavily on models that can represent heavy-tailed claim behaviour. Kenya's non-life insurance market is a useful setting for this problem: claim distributions are markedly skewed, catastrophic tail events occur, and policyholder portfolios are heterogeneous, all of which argue for flexible parametric severity models. This paper examines the Pareto Type II (Lomax) distribution as a severity model for Kenyan insurance claims, illustrated using a synthetic claims sample of 2,500 observations calibrated to reproduce the skewness and tail heaviness reported in the Kenyan motor, medical, property, and microinsurance literature. We develop a statistical and actuarial characterisation of the Pareto II model, including Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), Expected Shortfall (ES), and reinsurance pricing quantities, and compare four estimation approaches — maximum likelihood, L-moments, Bayesian inference, and a trimmed-likelihood estimator suited to contaminated data. Monte Carlo simulation is used to verify tail behaviour and to propagate parameter uncertainty into capital and reinsurance outcomes. The fitted tail index (α̂ ≈ 1.72) places the illustrative portfolio in the infinite-variance regime, and we show how proximity to the α = 2 boundary translates into solvency capital volatility, retention instability, and reinsurance pricing under Kenya's Risk-Based Supervision framework. The results are intended to demonstrate a decision-relevant methodology rather than to characterise the Kenyan market as a whole, and we set out the further validation against real portfolio data that would be needed before the findings could support market-wide conclusions. We close with directions for extending the framework to covariate-based, hierarchical Bayesian, machine-learning-augmented, and multivariate Pareto II structures.