Premium Estimation Under Model Uncertainty: Model Averaging for Left-Truncated Reinsurance Losses

In this paper, model averaging (MA) is proposed as a technique to address model uncertainty when estimating the premium for aggregate excess of loss reinsurance. Despite its intrinsic appeal, the use of MA in premium calculations involving left-truncated reinsurance losses remains largely unexplored. In this study, we examine the effectiveness of MA in estimating excess of loss premiums using both real-world data and Monte Carlo simulations. A model space of finite mixtures based on lognormal and gamma distributions is considered for fitting the left-truncated reinsurance losses. Premium estimates are computed based on all models in the considered model space. For a given retention level, closed-form solutions have been derived for the MA premium estimators based on gamma and lognormal mixtures. We examine how well MA estimators perform in comparison to estimators derived from the best model within a given model space, determined by criteria like the Akaike information criterion and Bayesian information criterion. This investigation offers an alternative approach for actuaries and risk managers to estimate premiums while taking model uncertainty into account.