Question

Acme Inc. owns a delivery truck worth $95,000. The truck is subject to the risk of physical damage, with the following loss probability distribution:

Annual Losses	Probability
$0	.85
$10,000	.10
$95,000	.05

Acme’s risk manager is considering three risk management options to manage this risk:

• Acme can purchase full insurance on this truck for the risk of physical damage up to a total loss of $95,000 for a premium of $3,500.
• Acme can purchase insurance with a limit of $95,000 and a deductible of $1,000 for a premium of $2,200.
• Acme is also considering retention as an alternative to full insurance.

1. Construct a loss matrix. All matrices must be constructed with the Risk Management Alternatives as the rows and the States of the World as the columns, as we did in the video. Ignore tax considerations for this assignment.

2. Suppose the risk manager wants to minimize expected loss as her decision rule. Which risk management alternative does she choose? Show all expected loss calculations and explain why the risk manager chooses a particular option.

3. Assume that the risk manager has a worry value (WV) equal to $1,500 for retention and a WV of $1,200 for deductible insurance. If the risk manager decides to minimize TOTAL COST, which risk management alternative does she choose? Show all total cost calculations and explain why the risk manager selects a particular option.

Answer 1

Loss Matrix

For retention, the loss is equal to the damage

For Full Insurance, the maximum loss is premium i.e 3500

For deductible insurance, the loss is premium i.e 2200 upto the deductible amount of 1000. Above deductible amount, it is Deductible+premium i.e 2200+1000= 3200

	State of the World
Risk Management	Zero Loss	Loss of $10,000	Loss of $95000
Full Insurance	3500	3500	3500
Deductible Insurance	2200	3200	3200
Retention	0	10000	95000

Expected Loss= Probability*Loss Amount

a) Full Insurance Expected Loss= (0.85*3500)+(0.1*3500)+(0.05*3500) = 3500

b) Deductible Insurance Expected Loss= (0.85*2200)+(0.1*3200)+(0.05*3200) = 2350

c) Retention Expected Loss= (0.85*0)+(0.1*10000)+(0.05*95000) = 5750

The manager aims to minimise expected Loss. That is why he should choose Deductible Insurance as it has the lease expected loss out of available 3 options

Total Cost= Monetary Cost(Expected Cost)+ Worry Value

a) Full Insurance Total Cost = 3500+0 = 3500 (worry value for full insurance is zero)

b) Deductible Insurance Expected Loss= 2350+1200 = 2550

c) Retention Expected Loss= 5750+1500 = 7250

The manager aims to minimise Total Cost. That is why he should choose Full Insurance as it has the lease Total Cost out of the 3 options.