Ellis Company owns a small office building worth $400,000. Cameron is the risk manager.
Ellis faces the risk of fire which would damage their building. The probability of a fire is
known to be 5%. If a fire occurs, there is a 25% chance of a full loss and a 75% chance of a
half loss ($200,000).
Cameron is considering the following risk management options to address the risk of fire to
their building:
a. Retention
b. Full Insurance for a premium of $15,000.
c. Partial Insurance with a premium of $12,000, a deductible of $2,000, and a face value of
$300,000.
d. Partial Insurance with a premium of $13,000, a deductible of $2,000, a coinsurance of
80/20, and an OOP max of $20,000.
•
Construct a loss matrix[4 points]
1
Ellis Company owns a small office building worth $400,000. Cameron is the risk manager.
Ellis faces the risk of fire which would damage their building. The probability of a fire is
known to be 5%. If a fire occurs, there is a 25% chance of a full loss and a 75% chance of a
half loss ($200,000).
Cameron is considering the following risk management options to address the risk of fire to
their building:
a. Retention
b. Full Insurance for a premium of $15,000.
c. Partial Insurance with a premium of $12,000, a deductible of $2,000, and a face value of
$300,000.
d. Partial Insurance with a premium of $13,000, a deductible of $2,000, a coinsurance of
80/20, and an OOP max of $20,000.
•
What is the expected loss for each option?[4 points]
•
What is the actuarially fair premium (AFP) in this case?[2 points]
2
Ellis Company owns a small office building worth $400,000. Cameron is the risk manager.
Ellis faces the risk of fire which would damage their building. The probability of a fire is
known to be 5%. If a fire occurs, there is a 25% chance of a full loss and a 75% chance of a
half loss ($200,000).
Cameron is considering the following risk management options to address the risk of fire to
their building:
a. Retention
b. Full Insurance for a premium of $15,000.
c. Partial Insurance with a premium of $12,000, a deductible of $2,000, and a coverage
limit of $300,000.
d. Partial Insurance with a premium of $13,000, a deductible of $2,000, a coinsurance of
80/20, and an OOP max of $20,000.
–
What worry value would make full insurance (
WV
F I
) preferable to partial insurance
with a coverage limit (
WV
IC
)? [2 points]
–
What worry value would make full insurance (
WV
F I
) preferable to partial insurance
with an OOP max (
WV
IO
)? [2 points]
–
What worry values would make retention (
WV
R
) preferable to partial insurance with an
OOP max (
WV
IO
)? [2 points]
3
Ellis Company owns a small office building worth $400,000. Cameron is the risk manager.
Ellis faces the risk of fire which would damage their building. The probability of a fire is
known to be 5%. If a fire occurs, there is a 25% chance of a full loss and a 75% chance of a
half loss ($200,000).
Cameron is considering the following risk management options to address the risk of fire to
their building:
a. Retention
b. Full Insurance for a premium of $15,000.
c. Partial Insurance with a premium of $12,000, a deductible of $2,000, and a face value of
$300,000.
d. Partial Insurance with a premium of $13,000, a deductible of $2,000, a coinsurance of
80/20, and an OOP max of $20,000.
Assume Cameron’s worry value for retention (
WV
R
) is $2,000, his worry value for insurance
with a coverage limit (
WV
IC
) is $1,000, and his worry value for insurance with an OOP max
(
WV
IO
) is $500.
–
If Cameron decides to minimize TOTAL COST, what risk management option does he
choose? [1 point]
–
What is Cameron’s PMAX for full insurance? [2 points]
–
During a meeting, the Chief Risk Officer (CRO) told Cameron that the most he would
pay for full insurance is $18,000. What is the CRO’s
WV
R
? [2 points]
–
Who is more risk averse, the CRO or Cameron? [2 points]
1.
| Loss | 0% | 25% | 50% | 100% |
| Amount | 0 | 100000 | 200000 | 400000 |
| Retention | 0 | 130000 | 260000 | 520000 |
| Full Insurance(15000) | 19500 | 19500 | 19500 | 19500 |
| Partial (12000) Deductible 2000 | 15600 | 18200 | 18200 | 18200 |
| Partial (13000)Deductible 2000 | 16900 | 19500 | 19500 | 19500 |
2.
Company should select Partial insurance with 12000 premium and 2000 deductible at occurrence. Because it has minimum loss/cost.
3.
Actuarially fair premium (AFP) in this case is 18200, being lowest value in full insurance.
4.
| Probability | 0.95 | 0.0375 | 0.0125 |
| Loss | 0% | 50% | 100% |
| Amount | 0 | 200000 | 400000 |
| Full Insurance(15000) | 19500 | 19500 | 19500 |
| WVF | 18525 | 731.25 | 243.75 |
Full insurance is prefered when WV >19500
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