Homework_Assignment_5

# Homework_Assignment_ - deductible will exceed the new deductible Determine the percent change in the expected value of the claim payment per

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Homework Assignment 5: (1) You are given: (i) Losses follow an exponential distribution with the same mean in all years. (ii) The loss elimination ratio this year is 70%. (iii) The deductible for the coming year is 4/3 of the current deductible. Compute the loss elimination ratio for the coming year. (Ans 80%) (The loss elimination ratio is defined as the ratio of the decrease in the expected payment with a deductible to the expected payment without the deductible.) (2) Loss amounts have the distribution function (x/100) 2 , 0 x 100 F(x) = 1 , 100 < x An insurance policy reimburses losses subject to a deductible of 11 up to a maximum reimbursement of 11. Calculate the expected reimbursement. (Ans 10.69) (3) For a distribution of losses you are given: x Pr(X x) E(X x) 50 0.40 40 75 0.50 50 100 0.60 65 150 0.80 82 200 0.90 95 1.00 110 An insurance policy reimburses a loss subject to a deductible of 50. The deductible is then raised so that only two-thirds of the number of losses that exceeded the old
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Unformatted text preview: deductible will exceed the new deductible. Determine the percent change in the expected value of the claim payment per payment random variable when the deductible is raised. (Ans Decrease of 3.57%) (4) For an insurance: (i) Losses have density function f X (x) = 0.02x when 0<x<10 and 0 elsewhere. (ii) The insurance has a deductible of 4 per loss. (iii) Y P is the claim payment per payment random variable. Calculate E[Y P ]. (Ans 3.43) (5) The total claim amount for a health insurance policy has an exponential distribution with λ = .001. The premium for the policy is set at 100 over the expected total claim amount. One hundred policies are sold. (a) Based on the normal approximation, what is the probability that the insurance company will have claims exceeding the premiums collected? (Ans 0.159) (b) Recalculate the probability based on the exact distribution of the insurance company’s claims. (Ans 0.158)...
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## This note was uploaded on 05/11/2011 for the course STOR 472 taught by Professor Charlesdann during the Spring '11 term at University of North Carolina School of the Arts.

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