The Balance Property in Insurance Pricing

Abstract

Unbiasedness, auto-calibration and the balance property are three important features that actuarial pricing algorithms should satisfy. Unbiasedness is a global property that describes price levels on average across the entire insurance portfolio. Auto-calibration is a local unbiasedness property that describes price levels on average on price cohorts. The balance property is a global property that describes price levels point-wise (in a P-almost sure sense). This paper focuses on the balance property. It is the easiest of the three to verify and to rectify, and it has a nice interpretation in terms of an allocation of the totally observed claims cost. We provide different methods of rectifying the balance property, and we discuss how these methods impact prediction accuracy. We find that there is not one method that is generally better than the others, thus, the chosen optimal method is a case by case choice.

Keywords: Unbiasedness, auto-calibration, balance property, actuarial pricing, regression, generalized linear model, GLM, neural network, maximum likelihood estimation, MLE