# hw9asol - Homework 9 Solutions 1 For each part a The...

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Homework 9 Solutions 1. For each part: a. The competitive premiums for each group would be their respective expected losses. Each policy-holder has a wealth level of 125, but a loss can reduce the wealth to 25; so expected losses are 75 (or 0.75*100) for the high-risk group and 25 (or 0.25*100) for the low-risk group. Note that in practice, the insurer would add an allowance for transaction costs and profit. b. Given the utility function: utility = sqrt(wealth), we get for the low risk group: i) utility with insurance =sqrt(125-25)=10, and ii) utility with no insurance is 0.75*sqrt(125)+0.25*sqrt(25)=9.635. For the high risk group: i) utility with insurance =sqrt(125-75)=7.071, and ii) utility with no insurance is 0.25*sqrt(125)+0.75*sqrt(25)=6.545. c. If there are an equal number of low and high risk drivers, then the insurer can break even by charging the average premium of 0.5*(25+75)=50. d.

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## This note was uploaded on 04/14/2009 for the course ISYE 4803 taught by Professor Staff during the Spring '08 term at Georgia Tech.

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hw9asol - Homework 9 Solutions 1 For each part a The...

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