Setting the price of an insurance good can be a perplexing problem. In manufacturing, the cost of a good is (relatively) known and provides a benchmark for assessing a market demand price. In other areas of financial services, market prices are available and provide the basis for a market-consistent pricing structure of products. In contrast, for many lines of insurance, the cost of a good is uncertain and market prices are unavailable. Expectations of the random cost is a reasonable place to start for a price, as this is the optimal price for a risk-neutral insurer. Thus, it has been traditional in insurance pricing to begin with the expected cost and to add to this so-called “margins” to account for the product’s riskiness, expenses incurred in servicing the product, and a profit/surplus allowance for the insurance company.
For some lines of business, especially automobile and homeowners insurance, analytics has served to sharpen the market by making the calculation of the good’s expectation more precise. The increasing availability of the internet among consumers has promoted transparency in pricing. Insurers seek to increase their market share by refining their risk classification systems and employing “skimming the cream” underwriting strategies. Recent surveys (e.g., Earnix (2013)) indicate that pricing is the most common use of analytics among insurers.
Underwriting, the process of classifying risks into homogenous categories and assigning policyholders to these categories, lies at the core of ratemaking. Policyholders within a class have similar risk profiles and so are charged the same insurance price. This is the concept of an “actuarially fair premium;” it is “fair” to charge different rates to policyholders only if they can be separated by identifiable risk factors. To illustrate, an early contribution by Bailey and LeRoy (1960) provided a catalyst to the acceptance of analytic methods in the insurance industry. This paper addresses the problem of classification ratemaking. It describes an example of automobile insurance that has five “use” classes cross-classified with four “merit rating” classes. At that time, the contribution to premiums for use and merit rating classes were determined independently of each other. Thinking about the interacting effects of different classification variables is a more difficult problem.