Non-life loss reserving models based on heavy-tailed distributions

The estimation of outstanding claims reserve is the core work of solvency management in Property & Casualty insurance companies. Common methods for claims reserving are generalized linear models (GLMs). However, traditional distributional assumptions of GLMs may not match actual incremental losses when the heavy-tailed feature exists, and meanwhile, dependencies among multiple run-off triangles also require a model to combine reserve assessments of individual lines of business (LoBs). This paper replaced traditional assumptions of gamma, lognormal and GB2 distributions with three new heavytailed distributions (i.e. exponentiated Fréchet distribution, generalized log-Moyal distribution and full tails Gamma distribution), investigated their application effects in outstanding claims reserving and finally applied Copula regressions to describe dependent structures among different LoBs. The predictive distribution and risk measurements of total reserves can be obtained by parametric bootstrap and Monte Carlo simulations. The empirical results based on an actual dataset show that, heavy-tailed distributions are of high values in improving the prediction of outstanding claims reserves, and the adjustment of reserves' dependencies makes the prediction more rational. © 2020, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.