{"id":5270,"date":"2016-05-07T12:20:34","date_gmt":"2016-05-07T17:20:34","guid":{"rendered":"http:\/\/www.ssc.wisc.edu\/~jfrees\/?page_id=5270"},"modified":"2016-12-29T09:33:51","modified_gmt":"2016-12-29T15:33:51","slug":"fund-claims-variables","status":"publish","type":"page","link":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/loss-data-analytics\/introduction-to-loss-data-analytics\/1-4-case-study-wisconsin-property-fund\/fund-claims-variables\/","title":{"rendered":"Claims Variables"},"content":{"rendered":"

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<\/em>. A positive amount, also known as the severity<\/em> of the claim, is a key financial expenditure for an insurer. The claim amount represents the reimbursement to the policyholder. <\/p>\n

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<\/em> 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. <\/p>\n

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). <\/p>\n

Table 1.2. 2010 Claims Frequency Distribution<\/span>\n\n\n\n\n\t\n\t\n\t\n\t
Type<\/td>Number of Claims<\/td><\/td><\/td><\/td><\/td><\/td><\/td><\/td><\/td>\n<\/tr>\n
Number<\/td>0<\/td>1<\/td>2<\/td>3<\/td>4<\/td>5<\/td>6<\/td>7<\/td>8<\/td>9 or more<\/td>Sum<\/td>\n<\/tr>\n
Count<\/td>707<\/td>209<\/td>86<\/td>40<\/td>18<\/td>12<\/td>9<\/td>4<\/td>6<\/td>19<\/td>1,110<\/td>\n<\/tr>\n
Proportion<\/td>0.637<\/td>0.188<\/td>0.077<\/td>0.036<\/td>0.016<\/td>0.011<\/td>0.008<\/td>0.004<\/td>0.005<\/td>0.017<\/td>1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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