Assignment \#7: Setting Loss Reserves and Developing Insurance Rates 1. Atwell Insurance expects that the general liability policies it selis in the current year will eventually result in $15 milion in incurred losses. To date. Atwell has paid only $5 million in losses. Determine the amount of loss reserves and loss. adjustment expense (LAE) reserves that are currently outstanding. (5 points) 2. Plate Glass Only Insurance ( PGO) has $50 million in earned premium from its plate glass insurance operations. PGO anticipates a 65 percent loss ratio and has known incurred losses of $15 million. Using the loss ratio method, estimated the the incurred but not reported (IBNR) reserve for PGO. (10 points) 3. In this table, complete the calculation of the incurred but not reported (IBNR) reserve using the percentage method. ( 5 points for each correct answer, total 25) 4. ABC Insurance Company has collected this historical data on its workers compensation claims for incurred losses. ( 000 omitted) (10 points for each correct answer, total 30 ) Estimate the incurred but not reported (IBNR) losses for 203 based on the historical data and using the average of the twelve-month loss development factors provided in the chart below as the selected values. Twelve-month ultimate loss development factor = Estimated ultimate losses = Incurred losses Ultimate loss development factors IBNR Reserve = Estimated ultimate losses - Incurred losses 5. Danforth Insurance Co. has an auto insurance portfolio consisting of 100,000 insured vehicles (exposure units) in a territory. Danforth analyzes the losses for this portfolio during a three-year period. a. If the dollar amount of total (incurred) losses is $30 million during the threeyear period identify what pure premium rate per exposure unit Danforth should use. ( 10 points) b. Assume that the reserves held to pay total (incurred) losses are inadequate by $3 million. Identify what the pure premium rate per exposure unit should be. (10 points) c. If Danforth used the rate based on an estimated $30 million in losses, identify what Danforth's loss would be the following year, assuming that the $33 million in total (incurred) losses was correct. (10 points) 6. Simon Insurance Company is reviewing their personal property premium for a territory. They know the following information: - Total losses =$7,734,375 - Loading percentage =20% - Properties insured =234,375 (exposure units) a. Using the methods discussed in class, What is the rate per exposure unit needed to cover losses and the loading percentage? Calculate the Pure Premium and the Gross Premium per exposure unit. ( 30 points, 15 points each part) Pure Premium: Gross Premium: Assignment \#7: Setting Loss Reserves and Developing Insurance Rates 1. Atwell Insurance expects that the general liability policies it selis in the current year will eventually result in $15 milion in incurred losses. To date. Atwell has paid only $5 million in losses. Determine the amount of loss reserves and loss. adjustment expense (LAE) reserves that are currently outstanding. (5 points) 2. Plate Glass Only Insurance ( PGO) has $50 million in earned premium from its plate glass insurance operations. PGO anticipates a 65 percent loss ratio and has known incurred losses of $15 million. Using the loss ratio method, estimated the the incurred but not reported (IBNR) reserve for PGO. (10 points) 3. In this table, complete the calculation of the incurred but not reported (IBNR) reserve using the percentage method. ( 5 points for each correct answer, total 25) 4. ABC Insurance Company has collected this historical data on its workers compensation claims for incurred losses. ( 000 omitted) (10 points for each correct answer, total 30 ) Estimate the incurred but not reported (IBNR) losses for 203 based on the historical data and using the average of the twelve-month loss development factors provided in the chart below as the selected values. Twelve-month ultimate loss development factor = Estimated ultimate losses = Incurred losses Ultimate loss development factors IBNR Reserve = Estimated ultimate losses - Incurred losses 5. Danforth Insurance Co. has an auto insurance portfolio consisting of 100,000 insured vehicles (exposure units) in a territory. Danforth analyzes the losses for this portfolio during a three-year period. a. If the dollar amount of total (incurred) losses is $30 million during the threeyear period identify what pure premium rate per exposure unit Danforth should use. ( 10 points) b. Assume that the reserves held to pay total (incurred) losses are inadequate by $3 million. Identify what the pure premium rate per exposure unit should be. (10 points) c. If Danforth used the rate based on an estimated $30 million in losses, identify what Danforth's loss would be the following year, assuming that the $33 million in total (incurred) losses was correct. (10 points) 6. Simon Insurance Company is reviewing their personal property premium for a territory. They know the following information: - Total losses =$7,734,375 - Loading percentage =20% - Properties insured =234,375 (exposure units) a. Using the methods discussed in class, What is the rate per exposure unit needed to cover losses and the loading percentage? Calculate the Pure Premium and the Gross Premium per exposure unit. ( 30 points, 15 points each part) Pure Premium: Gross Premium
