We have now seen the Fund’s two outcome variables, a count variable for the number of claims and a continuous variable for the claims amount. We have also introduced a continuous rating variable for coverage, a discrete quantitative variable for (logarithmic) deductibles, two binary rating variables for no claims credit and fire class, as well as two categorical rating variables for entity type and alarm credit. Subsequent chapters will explain how to analyze and model the distribution of these variables and their relationships. Before getting into the technical details, let us first think about where we want to go. General insurance company functional areas are described in Section 1.3; let us now think about how these areas might apply in the context of the property fund.
Initiating Insurance
Because this is a government sponsored fund, we do not have to worry about selecting good or avoiding poor risks; the fund is not allowed to deny a coverage application from a qualified local government entity. If we do not have to underwrite, what about how much to charge?
We might look at the most recent experience in 2010, where the total fund claims were approximately 28.16 million US dollars (=1377 claims x 20452 average severity). Dividing this total among 1,110 insureds suggests a premium of 24,370 ( (approx) 28,160,000/1110). However, 2010 was a bad year; using the same method, our premium would be much lower based on 2009 data. This swing in premiums would defeat the primary purpose of the fund, to allow for a steady charge that local property managers could utilize in their budgets.
Having a single price for all insureds is nice but hardly seems fair. For example, Table 1.7 suggests that Schools have much higher claims than other entities and so should pay more. However, simply doing the calculation on an entity by entity basis is not right either. For example, we saw in Table 1.8 that had we used this strategy, entities with a 15% alarm credit (for good behavior, having top alarm systems) would actually wind up paying more.
So, we have the data for thinking about the appropriate rates to charge but need to dig deeper into the analysis. We will explore this topic further in Chapter 6 on premium calculation fundamentals. Selecting appropriate risks is introduced in Chapter 7 on risk classification.