A Top-Down Approach to Understanding Uncertainty in Loss Ratio Estimation
By Alice M. Underwood, Jian-An Zhu
Abstract
In this paper we define a specific measure of error in the estimation of loss ratios; specifically, we focus on the discrepancy between the original estimate of the loss ratio and the ultimate value of the loss ratio. We also investigate what publicly available data can tell us about this measure. Using Other Liability Occurrence data as reported in Schedule P, we find that in a given accident year the values of this “estimation error ratio” for different companies are lognormally distributed. Furthermore, we find that the average accident year estimation error ratio is amenable to time series analysis. Using the time series analysis and the lognormal accident year model, we can estimate the distribution of possible estimation error ratios for the industry in a future year.
KEYWORDS: Schedule P, loss ratio, time series, ARIMA, Other Liability, estimation error, parameter risk