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ACTSC 431/831 – QUESTION SET 3
1. A groundup model of the losses has cdf
F
X
(
x
) = 1

1458000(45 + 2
x
)
(90 +
x
)
4
for
x
≥
0
.
The insurance policy calls for an ordinary deductible of 30 to be imposed.
Moreover, the
number of payments
N
P
has a logarithmic distribution with
β
= 7
/
4.
(a) On average, how many payments will be made on this policy?
(b) Show that the cdf of
Y
P
, the amount of payment given that a payment is made, is given
by
F
Y
P
(
y
) = 1

13824000(105 + 2
y
)
7(120 +
y
)
4
for
y
≥
0
.
(c) Discretize the severity distribution from part (b) using the method of rounding and an
interval of size 30. Determine all values up to a discretized amount paid of 150.
(d) Use the recursive formula to calculate the discretized distribution of aggregate payments
up to a discretized amount paid of 150.
2. A groundup model of the losses has cdf
F
(
x
) = 1

e

(
x/
100)
3
for
x
≥
0
.
The number of losses has a negative binomial distribution with
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 Spring '09
 laundriualt

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