Week 2 - Choice under uncertainty

Question 1

Diagram examples

Answer 1

See notes

Question 2

Describe what actuarily fair insurance is

Answer 2

• If an insurance contract is actuarily fair, the premium you pay for actuarily fair insurance reflects the true probability of the event occurring.
• This means that purchasing insurance leaves the expected value of the lottery or outcome the same for whether or not you have purchased insurance.

Question 3

Describe what actuarily unfair insurance is

Answer 3

• The premium you pay for the actuarily unfair insurance does not reflect the probability of the even where you would claim insurance happening.
• This means that purchasing insurance that is actuarily unfair will mean your expected wealth is less than if you hadn’t purchased the insurance.

Question 4

How can you calculate whether insurance is actuarily fair or not?

Answer 4

• Divide the premium of the insurance by the amount of insurance it covers and if this is equal to the probability then its actuarily fair.
• For example say a £1 premium covers £5 worth of insurance, and the probability of claiming insurance is 0.2. Then this would be actuarily fair as 1/5=0.2

Question 5

Worked example

Answer 5

See Notes