CAS Exam 8 Fall 2012, Question 15
Study guide: Exam 8
An actuarial consulting firm is reviewing the inflation assumption used by a large insurer that writes casualty excess of loss coverage. The consulting firm has made the following assumptions regarding the insurer's excess casualty book:
- Overall inflation is 8.0% and is assumed to have the same multiplicative effect on each size of loss.
- The unlimited, ground-up loss severity for the book of business follows a lognormal distribution with the expected loss equal to $5,890,000.
- The following limited average severities, based on a lognormal distribution, apply to the insurer's excess casualty book:
Per occurrence limit k |
E[g(x;k)] |
E[g(x;k/1.08)] |
|---|---|---|
| $1,000,000 | 715,812 | 675,097 |
| $2,000,000 | 1,170,998 | 1,112,349 |
| $3,000,000 | 1,513,415 | 1,444,181 |
| $10,000,000 | 2,800,239 | 2,710,132 |
| $20,000,000 | 3,613,385 | 3,524,644 |
| $30,000,000 | 4,063,944 | 3,981,081 |
| $40,000,000 | 4,359,735 | 4,282,929 |
| $50,000,000 | 4,571,783 | 4,500,504 |
Part a (1 point)
Using the consulting firm's assumptions, calculate the average increase in excess losses due to inflation for a policy with a $10,000,000 limit attaching at $30,000,000.
Part b (0.75 points)
The insurer agrees with the consulting firm's overall trend assumption and general methodology, but believes that the average increase calculated in part a. above is too high. Describe any differences in assumptions the insurer may have with the consulting firm.
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