8.1 For the excess loss variable,
For the left censored and shifted variable,
and it is interesting to note that the excess loss variable has an exponential distribution.
8.2 For the per-payment variable,
For the per-loss variable,
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,
The ratio is then
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 ...