ACT 420 Problem Set 3

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Arizona State University *

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Accounting

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Apr 24, 2024

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ACT 420 Problem Set 3 Loss Adjustments Instructions: submit your solutions to the following problems as an Excel file in Canvas. You should be able to copy data tables in these problems to Excel. 1. Given the following data: Claim Number Loss Amount 1 10000 2 15000 3 30000 4 35000  Basic Limit = $25,000  Total limits severity trend = 10% Calculate the excess loss trend. [Hint: how do capped and uncapped total losses change after application of the trend factor?] 2. The current workers compensation indemnity benefit structure in a state is:  The compensation rate is 80% of the workers pre-injury wage.  The state average weekly wage (SAWW) is currently $1,500.  The minimum benefit is 50% of SAWW  The maximum benefit is 125% of SAWW The following changes have been proposed to the benefit structure:  The proposed minimum benefit is 75% of SAWW  The proposed maximum benefit is 100% of SAWW The distribution of wages for injured workers for Company A is: Ratio to SAWW # Workers Total Weekly Wages <50% 150 $ 108,750 50% - 75% 100 $ 110,000 75% - 100% 95 $ 137,750 100% - 125% 50 $ 87,500 >125% 45 $ 216,000 Total 440 $ 660,000 Calculate the impact to Company A of the proposed benefit change. (If you need to split a category, assume 50% of workers are in each subcategory.)

3. An actuary is calculating a rate change to be effective 7/1/2020. Given the following:  Policies are written on a semi-annual basis.  Rates are expected to be in effect for one year.  The exposure base is non-inflationary.  The annual frequency and severity exponential trend fits based on data for the 12 months ending each quarter evaluated through 12/31/2018 are: Number of Points Frequency Exponential Fit Severity Exponential Fit 20 points -2.9% 3.4% 16 points -3.2% 3.0% 12 points -2.5% 2.8% 8 points -0.5% 2.9% 6 points 3.0% 3.1% 4 points 2.8% 3.3% Calculate a pure premium trend factor that applies to accident year 2016, justifying the selected trends and methodology. 4. Given the following information about two claims: Claim Number Accident Date Transaction Date Payment Ending Reserve 1 1/1/2019 1/1/2019 $ - $ 20,000 1 1/1/2019 1/1/2020 $ 25,000 $ - 2 4/1/2019 7/1/2019 $ - $ 50,000 2 4/2/2019 10/1/2019 $ 25,000 $ 75,000 2 4/3/2019 4/1/2020 $ 100,000 $ 20,000 a) Calculate the incurred losses for accident year 2019 as of 5/1/2020 b) Calculate the incurred losses for calendar year 2019 and calendar year 2020 5. Given the following information for an insurance company as of 12/31/2016: Accident Year Earned Premium (,000) Reported Loss (,000) Cumulative Development Factors 2012 $ 3,000 $ 1,500 1.05 2013 $ 3,500 $ 1,925 1.10 2014 $ 3,300 $ 1,749 1.20 2015 $ 3,200 $ 1,984 1.35 2016 $ 3,800 $ 2,470 1.40  All policies are annual  Annual loss cost trend = 3% Calculate the trended, developed average losses that could be used to develop rates that would be in effect for one year beginning 1/1/2018.

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