The COTOR Challenge, Round 4

Round 4 Challenge Announcement

History

In the spring of 2004 a challenge was issued to members of the VALCON CAS e-mail list. Hypothetical loss observations were simulated from a distribution. A sample of 250 such "observations" was supplied to the members of the e-mail list, with the challenge of estimating the frequency, expected claim severity and pure premium of the 500 x 500 layer. A number of interesting approaches were tried and a lively discussion about extreme value analysis took place.

In the fall of 2004 COTOR issued another challenge under well defined conditions. A sample of 250 claims was randomly generated from a distribution by Stuart Klugman. The challenge was to estimate the average severity and 95 percent confidence intervals for the $5 million xs $5 million layer. Information about the true distribution and its parameters was not disclosed until the presentation of solutions at the November 2004 CAS meeting.

At the time of the Round 2 it was realized that it is not easy to make these estimations and that real world problems are even more challenging than this because of trend and development (considerations eliminated from round 2), potential unforeseen changes in the environment, and the fact that 250 real world claims would likely not follow any known distribution.

In Round 3 of the challenge COTOR addressed some of the real world issues identified above and made the challenge a bit more "challenging".

Seven consecutive years of claims were drawn at random from a heavy tailed distribution by our loss distribution expert, Stuart Klugman. A total of 490 claims were sampled, split amongst the 7 years. Each year of claims was drawn from the same distribution, except that the scale parameter changed each year due to inflation.

The challenge was to estimate the mean severity and calculate 95 percent confidence and prediction intervals for the $500,000 xs $500,000 layer for the next (eighth) year.

Round 4 Description

Round 4 promises to be the most "challenging" challenge to date.

In this round 500 claims per year for 5 years have been randomly generated. The following is known about the underlying distribution:

• The distribution is either a mixture of two distributions, one with a longer tail then the other or is a single, long tailed distribution.
• The non-scale parameter(s) does not ordinarily change over time.
• The scale parameter(s) are affected by inflation. If it is a mixture distribution, the same inflation rate applies each year to both distributions. The expected rate of inflation is constant from year to year and the yearly inflation rates are independent.
• It is believed that something happened in year four to change the distribution. Based on an understanding of this line of business and events in that year, there seem to be three valid possibilities. One is that a mixture of two distributions is correct and that the change is in the weight assigned to each, while the parameters of the individual distributions (except for the inflation effect on the scale parameters) are unchanged.

Another possibility is there is a single distribution and some or all of the parameters have changed. A final possibility is that nothing at all has changed and that the jump in the average loss in year four is merely normal statistical fluctuation.

Your task is to estimate the expected loss for year 6 in the layer $500,000 excess of $500,000 assuming that the distribution from year 5 will not change (except for inflation) and the inflation assumption does not change. Then place 95 percent confidence and prediction intervals about your estimate. Be sure to defend the choice of scenario from item 4 and consider commenting on the sensitivity of your results to the three options.

Winners will be selected by a committee of COTOR members. Criteria will include accuracy of their estimates, use of interesting and innovative approaches, clarity of the description, as well as ease of use of the approach. Winners will be asked to present their approach in person at the November, 2006 CAS meeting in San Francisco, California.

Closing date for submission of your response to the challenge is October 15, 2006.

Please submit your response to the challenge to challenge@casact.org. A brief description of the approach (a paragraph or 2) should accompany your solution to the problem. Spreadsheets containing examples of the calculation are welcome.

The spreadsheet with claim data can be downloaded.