Forum Administrator
Group: Forum Members
Active: 9/4/2010
Posts: 2,194 |
|
Teng and Perkins, estimating the premium asset, 20X5 exam problem (The attached PDF file has better formatting.) CAS Fall 2005 Exam 6, Question 20 (3 points) You are given the following information as of December 31, 20X4: Retro Adjustment Period | Selected PDLD Ratio | Incremental Loss Emerged | First | 1.600 | 82.6% | Second | 0.800 | 12.8% | Third | 0.200 | 4.2% | Subsequent | 0.000 | 0.4% | | | 100.0% |
Policy Period | Expected Future Loss Emergence | Premium Booked from Prior Adjustments | Premium Currently Booked | 20X1 | $0 | $125,467 | $125,467 | 20X2 | $12,000 | $120,248 | $120,679 | 20X3 | $28,000 | $114,968 | $116,328 | 20X4 | $160,000 | $0 | $172,763 | | $200,000 | $360,683 | $535,237 |
All policies are effective on January 1. The first retro adjustment is booked 18 months after the policy effective date and subsequent adjustments are booked at twelve month intervals thereafter. Using the method described by Teng and Perkins, calculate the total premium asset for policy periods 20X1 through 20X4 as of December 31, 20X4. Solution: We solve the problem in three steps: We derive CPDLD ratios as weighted averages of the PDLD ratios, where the weights are the expected loss emergence in the retro adjustment period. We derive the future premiums as the expected future loss emergence times the CPDLD ratios by policy period. We adjust the future premiums by premiums booked between adjustment dates. Step #1: CPDLD ratios are weighted averages of the PDLD ratios, where the weights are the expected loss emergence in the retro adjustment period. We proceed from the last retro period: Subsequent: 0.000Third: (0.200 × 4.2% + 0.000 × 0.4%) / (4.2% + 0.4%) = 0.183 Second: (0.800 × 12.8% + 0.200 × 4.2% + 0 × 0.4%) / (12.8% + 4.2% + 0.4%) = 0.637 First: (1.600 × 82.6% + 0.800 × 12.8% + 0.200 × 4.2% + 0.000 × 0.4%) / (82.6% + 12.8% + 4.2% + 0.4%) = 1.432 Jacob: Must we show this calculation on the exam? Rachel: Say what you are doing and show the calculation for one period. It is a waste of exam time to write out the arithmetic for each year. Step #2: Future premiums are the expected future loss emergence times the CPDLD ratios by policy period. More precisely, these are the future premiums if policyholders’ surplus are booked only at retrospective adjustment dates. 20X1: $0 × 0.000 = $0 20X2: $12,000 × 0.183 = $2,196 20X3: $28,000 × 0.637 = $17,836 20X4: $160,000 × 1.432 = $229,120 Step #3: We adjust the future premiums by premiums booked between adjustment dates. Consider policy year 20X3: We expect $28,000 of additional losses to be reported, for which we expect $28,000 × 0.637 = $17,836 of additional premium. This premium is in addition to the premium booked by the last adjustment date, which was $114,968 by June 30, 20X4. By December 31, an additional premium of $116,328 – $114,968 = $1,360 had already been booked, so the unbooked premium asset for 20X3 is $17,836 – $1,360 = $16,476.
|
|
Home
Login
Register
Member List