Homework Assignment 6:
(1)
For 2003, loss sizes follow a uniform distribution with f(x) = 1 / 2500, 0 < x < 2500.
Inflation of 3% impacts all losses uniformly from 2003 to 2004.
In 2004 a deductible of
100 is applied to all losses.
Determine the expected value of the claim payment in 2004
in the event that a loss is incurred. (Ans 1189.44)
(2)
Losses in 2003 follow a twoparameter Pareto distribution with
α
= 2 and
θ
= 5.
Losses
in 2004 are uniformly 20% higher than in 2003.
An insurance covers each loss subject to
a deductible of 10.
Calculate the Loss Elimination Ratio in 2004.
(Ans 0.625)
(Recall that the parameter
θ
is a scale parameter.)
(3)
Loss amounts in the year 2000 have the distribution function
(x/100)
2
,
0
≤
x
≤
100
F(x) =
1
,
100 < x
Losses are uniformly 10% higher in 2001.
An insurance policy reimburses losses subject to a deductible of 11 up to a maximum
reimbursement of 11.
Calculate the expected reimbursement for a loss in 2001. (Ans 10.74)
(4)
A population is equally divided into two classes of drivers.
The number of accidents per
individual driver is Poisson for all drivers.
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 Spring '11
 CharlesDann
 Variance, Probability theory, Exponential distribution

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