Problem -
A firm has the following probability distribution for annual losses due to vandalism. All amounts are before any tax consideration. The firm has a tax rate of 20%.
|
Annual Losses
|
Probability
|
|
$ 0
|
.75
|
|
$ 4,000
|
.20
|
|
$ 10,000
|
.05
|
The firm is considering three options:
1. Retention
2. Deductible insurance, Face amount = $10,000, Deductible = $300, Premium = $1300.
3. Full insurance, Face amount = $10,000, Premium = $1500
1. Derive the after-tax loss matrix for the firm.
2. If the risk manager's decision rule is to minimize after-tax expected cost, which option will she choose? Show why?
3. What worry value retention would make the full insurance alternative preferable to retention? Be sure to explain your numerical answer.
4. What worry value or values would make deductible insurance preferred to retention? Be sure to explain your numerical answer.
5. What is the after-tax actuarially fair premium in this example?
6. Consider retention and deductible insurance. Which of these options would have the highest worry value?
7. Suppose the risk manager has a choice between full insurance and retention. If her worry value for retention is $500, what is the maximum premium she would pay (after tax) for full insurance?
8. During a meeting, the CRO in this firm told you that the maximum premium he would pay (after tax) for full insurance would be $1700. Derive his worry value for retention.
9. Who is more risk averse? The CRO or the risk manager? Explain your answer.