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Student Solutions Manual to Accompany Loss Models: From Data to Decisions, Fourth Edition by Gordon E. Willmot, Harry H. Panjer, Stuart A. Klugman

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CHAPTER 8

CHAPTER 8 SOLUTIONS

8.1   SECTION 8.2

8.1 For the excess loss variable,

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For the left censored and shifted variable,

image

and it is interesting to note that the excess loss variable has an exponential distribution.

8.2 For the per-payment variable,

image

For the per-loss variable,

image

8.3 From Example 3.1 E(X) = 30,000 and from Exercise 3.9,

image

Also F(5,000) = 1 − 0.3е−0.00001(5,000) = 0.71463, and so for an ordinary deductible the expected cost per loss is 28,536.88 and per payment is 100,000. For the franchise deductible, the expected costs are 28,536.88 + 5,000(0.28537) = 29,963.73 per loss and 100,000 + 5,000 = 105,000 per payment.

8.4 For risk 1,

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The ratio is then

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As k goes to infinity, the limit is infinity.

8.5 The expected cost per payment with the 10,000 deductible is

At the old ...

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