Introduction

Models describing variation in claim size lack the theoretical underpinning provided by the Poisson point process. The traditional approach is to impose a family of probability distributions and estimate their parameters from historical claims z1, …, zn (corrected for inflation if necessary). Even the family itself is often determined from experience. An alternative with considerable merit is to throw all prior mathematical conditions overboard and rely solely on the historical data. This is known as a non-parametric approach. Much of this chapter is on the use of historical data.

How we proceed is partly dictated by the size of the historical record, and here the variation is enormous. With automobile insurance the number of observations n might be large, providing a good basis for the probability distribution of the claim size Z. By contrast, major incidents in industry (like the collapse of an oil rig) are rare, making the historical material scarce. Such diversity in what there is to go on is reflected in the presentation below. The extreme right tail of the distribution warrants special attention. Lack of historical data where it matters most financially is a challenge. What can be done about it is discussed in Section 9.5.