CAS Exam 8 Fall 2018, Question 2
Study guide: Exam 8
A certain golf course holds a series of tournaments throughout the year, during which prizes are awarded if a player hits a hole-in-one. The prize amounts vary based on the difficulty of the hole, but are consistent across tournaments.
The course has approached an insurer to design a policy which would protect the course from large prize payouts. The insurer would pay the full prize amount directly to the winning player, and seek recoveries of any applicable deductible from the golf course.
A single annual policy will cover all of the tournaments throughout a given year.
The total number of holes-in-one in a given year (n), across all tournaments, has the following probability distribution:
n |
P(n) |
|---|---|
| 0 | 0.80 |
| 1 | 0.15 |
| 2 | 0.05 |
| 3 or more | 0.00 |
Given that a hole-in-one has occurred, the prize amount (x) has the following probability distribution:
x |
P(x) |
|---|---|
| $100,000 | 0.40 |
| $250,000 | 0.35 |
| $500,000 | 0.24 |
| $1,000,000 | 0.01 |
The expenses and profit for this policy are:
| Fixed Expenses | None |
|---|---|
| General Expenses | 8% of premium |
| Commission | 10% of premium |
| Taxes | 5% of premium |
| Underwriting Profit | 5% of premium |
The above assumptions apply to all program structures.
Part a (1 point)
Calculate the annual guaranteed cost premium for this policy.
Part b (1 point)
Calculate the annual premium for this policy under a $100,000 per-occurrence deductible.
Part c (1.75 points)
Calculate the annual premium for this policy under a $1,000,000 annual aggregate deductible and no per-occurrence deductible.
Part d (1 point)
Calculate the annual premium for this policy under a $250,000 franchise deductible.
Part e (1 point)
Explain which of the deductible structures above would generate the greatest credit risk to the insurer, and estimate the magnitude of that risk.
Part f (1.25 points)
The insurer has allocated $45,000 of capital to support the guaranteed cost policy in part a. above.
Recommend and justify which of the three options below would be the most appropriate capital requirement to support the per-occurrence deductible policy in part b. above:
i. $45,000
ii. $32,000
iii. $19,000
Part g (2.5 points)
Based on the success of this program, the insurer wishes to expand this coverage to other golf courses.
The insurer will offer varying per occurrence limits with no aggregate limits, the prize amounts would remain the same, and the same distribution assumptions would apply.
Using $100,000 as a basic limit, use the variance method to calculate the risk-loaded ILF for a $500,000 policy limit. Assume \rho(100{,}000) = 5{,}750 and use k = 0.0000005.
Answer this question and see the worked solution