CAS Exam 7 Spring 2014, Question 5
Study guide: Exam 7
An insurance company has 1,000 exposures uniformly distributed throughout the accident year. The a priori ultimate loss is $800 per exposure unit.
The expected loss payment pattern is approximated by the following loglogistic function where G is the cumulative proportion of ultimate losses paid and x represents the average age of reported losses in months.
G(x) = \dfrac{x^{\omega}}{x^{\omega} + \theta^{\omega}}\omega = 2.5\theta = 24
Part a (1 point)
Calculate the expected losses paid in the first 36 months after the beginning of the accident year.
Part b (0.75 points)
Assume the actual cumulative paid losses at 36 months after the beginning of the accident year are $650,000. Estimate the ultimate loss for the accident year using assumptions based upon the Cape Cod method.
Part c (0.5 points)
Estimate the ultimate loss for the accident year based on the loglogistic payment model and the actual payments through 36 months, disregarding the a priori expectation.
Part d (1 point)
Calculate a reserve estimate for the accident year by credibility-weighting the two estimates of ultimate loss in parts b. and c. above using the Benktander method.
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