Claims Variables

At a fundamental level, insurance companies accept premiums in exchange for promises to indemnify a policyholder upon the uncertain occurrence of an insured event. This indemnification is known as a claim. A positive amount, also known as the severity of the claim, is a key financial expenditure for an insurer. The claim amount represents the reimbursement to the policyholder.

Ignoring expenses, an insurer that examines only amounts paid would be indifferent to two claims of 100 when compared to one claim of 200, even though the number of claims differ. Nonetheless, it is common for insurers to study how often claims arise, known as the frequency of claims. The frequency is important for expenses and influences contractual parameters that are written on a per occurrence basis such as deductibles and policy limits. Claims frequency is routinely monitored by insurance regulators and can be a key driver in the overall indemnification obligation of the insurer. We shall consider the two claims variables, the severity and frequency, as the two main outcome variables that we wish to understand, model, and manage.

To illustrate, in 2010 there were 1,110 policyholders in the property fund. Table 1.2 shows the distribution of the 1,377 claims. Almost two-thirds (63.7%) of the policyholders did not have any claims and an additional 18.8% only had one claim. The remaining 17.5% (=1 – 0.637 – 0.188) had more than one claim; the policyholder with the highest number recorded 239 claims. The average number of claims for this sample was 1.24 (=1377/1110).

Table 1.2. 2010 Claims Frequency Distribution

TypeNumber of Claims
Number0123456789 or moreSum
Count70720986401812946191,110
Proportion0.6370.1880.0770.0360.0160.0110.0080.0040.0050.0171


There are two common approaches for examining the distribution of the claims severity. One common approach is to examine each of the 1,377 claims and construct a distribution from this sample. Another common approach is to examine each insured with at least one claim and construct a distribution from each insured’s average claim. In our 2010 sample, there were 403 (=1110-707) such policyholders. For 209 of these policyholders with one claim, the average claim equals the only claim they experienced. For the policyholder with highest frequency, the average claim is an average over 239 separately reported claim events. The total severity divided by the number of claims is also known as the pure premium or loss cost.

Table 1.3 summarizes the sample distribution of average severities from the 403 policyholders; it shows that the average claim amount was 56,330 (all amounts are in US Dollars). However, the average gives only a limited look at the distribution. More information can be gleaned from the summary statistics which show a very large claim in the amount of 12,920,000. Figure 1.2 provides further information about the distribution of sample claims, showing a distribution that is dominated by this single large claim so that the histogram is not very helpful. Even when removing the large claim, you will find a distribution that is skewed to the right. A generally accepted technique is to work with claims in logarithmic units especially for graphical purposes; the corresponding figure in the right-hand panel is much easier to interpret.

Table 1.3. 2010 Average Severity Distribution
MinimumFirst QuartileMedianMeanThird QuartileMaximum
1672,2264,95156,33011,90012,920,000
Figure 1.2: Distribution of Positive Average Severities.
Figure 1.2: Distribution of Positive Average Severities.

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