3640-002 Midterm 1 ~ with Answers(1)

MATH 3640 – Mid-Term 1 Show your work! I give partial credit! Use the following three years of information to answer questions 1-3: Claim Accident Year 1 2020 6/1/2020 2,000 4,000 1 1/1/2020 6/30/2020 55,000 1 2020 7/1/2021 4,000 8,000 2 10/1/2020 3/31/2021 10,000 1 2021 7/1/2022 7,000 6,000 3 11/15/2020 5/15/2021 2,600 2 2020 5/1/2020 10,000 22,000 4 10/1/2021 3/31/2022 65,200 2 2020 7/1/2021 12,000 0 5 10/1/2021 3/31/2022 51,420 2 2021 3/1/2021 9,000 5,000 6 6/15/2022 12/15/2022 20,320 2 2021 3/1/2022 8,810 1,500 3 2020 3/1/2022 5,000 0 5% Annual Loss Trend 3 2022 5/15/2022 0 20,500 2% Annual Premium Trend 4 2020 7/1/2020 0 500 9% LAE as a percentage of losses 4 2021 7/1/2021 6,240 1,260 6% Variable Expense Ratio 4 2022 10/15/2022 2,520 2,490 15% Profit & Contingencies Provision Rate Change History Incurred Cumulative Development Factors Rate Change 1/1/2021 12% 36-Ult (for 2020 data) 1.1 Rate Change 4/1/2021 3% 24-Ult (for 2021 data) 1.3 Law Mandate 7/1/2021 -5% 12-Ult (for 2022 data) 1.6 Rate Change 7/1/2022 8% Rate Change 1/1/2023 10% Law Mandate 4/1/2023 -5% - All policies are semi-annual - Assume that exposures are written evenly throughout each calendar year - Fixed expenses are $15000 Transaction Date Loss Payment Case Reserve as of Transaction Date Policy Group Effective Date Expiration Date Written Premium - Rates will be in effect for 2.5 years with a proposed effective date of 10/1/2024

auto policy’s required deductible. to one-step trending. may be preferred over the Loss Ratio Method. Find the Direct Effect of the proposed changes to WC indemnity benefits: - Compensation rate is decreasing from 90% to 80% of the worker's pre-injury wage - State average weekly wage (SAWW) is $800 - Distribution of workers (and their wages): <50% 50 23,000 50-75% 300 170,000 75-100% 400 250,000 100-125% 200 240,000 125-150% 100 210,000 1) (23 points) Prepare the loss data for an indication by doing the following: i. Aggregate the historical incurred losses for AY 2020, 2021, and 2022 as of today ii. Develop the losses to ultimate iii. Use one-step trending to trend the losses to the prospective period (provide the dates us iv. Sum the three ultimate, trended accident year losses 2) (50 points) Prepare the premium data for an indication by doing the following: i. Calculate the earned premiums for CY 2020, 2021, and 2022 ii. Use the parallelogram method to on-level the earned premiums iii. Use one-step trending to trend the earned premiums to the prospective period (provide the dates used for "earned to earned" AND "written to written") iv. Sum the three onleveled, trended calendar year earned premiums 3) (9 points) With the answers from #1 & #2, calculate the indicated change using the Loss Ratio Method. 4) (5 points) What is meant by “Ratemaking is prospective and must balance at the aggregate and individual levels”? 5) (4 points) Provide one example of a direct effect and one example of an indirect effect from an increase to an 6) (5 points) Briefly describe the typical treatment of shock losses & catastrophe losses in ratemaking analysis. 7) (2 points) Provide an example of a time when using two-step premium trending may be preferred 8) (2 points) Provide an example of a time when using the Pure Premium Method for indication calculation BONUS (4 points) - Minimum indemnity benefit is decreasing from 90% to 80% of the SAWW - Maximum indemnity benefit is increasing from 112.5% of the SAWW to 120% of the SAWW Ratio to Avg Weekly Wage Number of Workers Total Weekly Wages