Estimating the Parameter Risk of a Loss Ratio Distribution

Actuaries commonly build statistical models to predict future experience. To do this a model must be chose, and parameters for that model must be calculated and selected. This paper assumes that the correct model has been chosen, but looks at the risk taken by assuming that the selected parameters accurately represent the true underlying distribution. A bootstrapping methodology is used to estimate the parameter risk associated with a loss ratio distribution. The results provide an estimate of the parameter risk of the ground-up loss ratio and for excess loss ratio layers commonly known as aggregate stop loss contracts. The paper shows that the impact of parameter risk on expected losses can be significant especially for aggregate stop loss contracts.