UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGNCollege of Commerce and Business Administration D E P A R T M E N T O F F I N A N C EFinance 341 Assignment 2Spring, 2002 Due: February 12, 2002The first four questions are based on the following cumulative loss payment information for an automobile insurer. Assume that no further development occurs after 96 months. The auto liability earned premiums for 2001 are $70,515,677. The expected loss ratio for 2001 is 87.0%. Use the average link factors to determine the age-to-ultimate factors. (If you are not using a spreadsheet program to do these calculations, round the link factors to three decimal places.) Cumulative Loss Payments for Auto Liability(000 omitted)Development Age (Months)Accident Year12 24 36 48 60 72 84 961994 13,25525,70631,66634,66336,13536,82737,18337,3531995 14,32127,55333,49636,52438,04138,82439,2031996 15,63429,65535,85039,00340,72041,4911997 17,21331,80338,13841,60743,4041998 17,86232,40238,98642,6431999 18,48533,12839,9222000 18,71833,4952001 19,295 1. Calculate the loss reserve for accident year 2001 using the expected loss ratio method.2. Calculate the loss reserve for accident year 2001 using the Bornhuetter-Ferguson method.3. Calculate the loss reserve for accident year 2001 using the Paid Loss Development method.4. Which of the values calculated above do you feel is the best estimate of theneeded loss reserves for accident year 2001? Why?5. Calculate the percent rate change that is indicated using the loss ratio method based on the following experience:Actual loss ratio 85.3%Expected loss ratio 79.7%6. Calculate the indicated gross premium using the pure premium method based on the following information:Loss frequency 3%Loss severity 5,780Fixed expenses 75Variable expenses (including profit) 16%7. The incurred losses for a given line of business were $78,950,000 in 2000 and the earned exposures were 58,000. The actuary is trending these losses for 3 years to use in a rate filing. If loss frequency is declining at a rate of 1.5% per year and loss severity is increasing at a rate of 3.8% per year, what is the trended pure premium?8. You are a line underwriter for a property-liability insurer. You receive an application for homeowners insurance coverage from a new customer. The only concern you have about writing this policy is that the family owns two dogs. List two questions you would ask the applicant before deciding whether or not to accept this application.For the next two questions, you may use either the State Farm Car Policy we usedin Finance 260 or the Personal Auto Policy included as Appendix B in the text. (Indicate which one you used in your answer.) Also, use the Homeowners 3 Special Form Policy in Appendix A of the text. You are the claims representative for an insurance company that has written both homeowners insurance and auto insurance for Jim Olds. Jim’s nephew, Paul, is visiting from Colorado during winterbreak and staying with Jim. Paul is an avid skier, and Jim is trying to give him a chance to ski while staying in central Illinois. After several inches of snow falls, Jim shovels all the snow in his backyard into a small hill (very small). Paul tries to ski down this snow pile, but runs into the side of Jim’s garage, breaking a finger. Jim takes Paul to the emergency room for treatment. Later, Jim decides a better way to let Paul ski would be to tow him around the neighborhood behind his car. This works well for the first three circles around the block, but on the fourth circuita snowplow suddenly comes around a corner, forcing Jim to hit the brakes. Paul skis into a tree, breaking his arm. He has to be hospitalized for this injury. For thenext two questions, indicate whether the situation is a first or third party claim and whether or not it would be covered. If the claim would be covered, indicate whether the auto policy or the homeowners policy would pay the claim.9. The emergency room bill for x-rays and setting Paul’s broken finger is $1500. Paul does not sue Jim for this accident.10. The medical bills for Paul’s broken arm are $10,000. Paul sues Jim for this accident, and a court awards Paul $30,000 for his injuries.Fin 341 - Assignment 2 Answer Sheet Name_________________________(This sheet is for your answers only. Attach it to the front of your