Question

Brad owns a Van Gogh masterpiece worth $5 million. There is a 1% chance the painting will get stolen, leaving Brad with nothing.

What is the expected value of this gamble?
What is the minimum insurance premium an insurance company would charge to fully insure the painting against theft? (Note: minimum insurance premium = fair insurance premium = Expected loss)

Brad's certainty equivalent for this risky situation is $4,900,000. What is the maximum insurance premium he'd be willing to pay for full insurance?

Answer 1

A).

Consider the given problem here Brad owns a Van Gogh masterpiece of worth “$5 million” and there is a chance that the painting will get stolen, => the expected value of gamble is given by.

=> EV = $5 million*0.99 + 0*0.01 = 5,000,000*0.99 = $4,950,000 = $4.95 million.

B).

Now, the minimum insurance premium is given by the expected loss. So, here there is 1% probability that the masterpiece will be stolen and will have noting, => the expected loss is given by “$5 million*0.01 = $50,000”. So, the minimum insurance premium is given by “$50,000”.

C).

Now, if Brand’s certainty equivalent is “$4,900,000”, => the maximum insurance premium is given by “5,000,000-4,900,000 = $10,000”.