Question

Yuri owns just one ship, he calls it Previt. The ship is worth $25 million dollars. If the ship sinks, Yuri loses $25 million. The probability that it will sink is .02. Yuri's total wealth, including the value of the ship is $50 million. He is an expected utility maximizer with utility U(W) equal to W2. What is the maximum amount that Yuri would be willing to pay in order to be fully insured against the risk of losing his ship

Answer 1

$745,000

Step-by-step explanation:

Calculation to determine the maximum amount that Yuri would be willing to pay in order to be fully insured against the risk of losing his ship

First step is to calculate the Expected Utility (√W)

Expected Utility = (98% x √$25,000,000) + (2% x √$0)

Expected Utility = $4,900

Second step is to calculate the Fair premium of insurance policy using this formula

Fair premium of insurance policy = Probability of loss x Size of loss

Let plug in the formula

Fair premium of insurance policy = 2% x $25,000,000

Fair premium of insurance policy = $500,000

Third step is to calculate the Maximum premium using this formula

Maximum premium = Maximum utility - Expected Utility²

Let Plug in the formula

Maximum premium = $25,000,000 - $4,900²

Maximum premium = $25,000,000 - $24,010,000

Maximum premium= $990,000

Now let calculate the Maximum amount willing to pay using this formula

Maximum amount willing to pay = (Fair premium + Maximum premium) / 2

Let plug in the formula

Maximum amount willing to pay= ($ 500,000 + $990,000) / 2

Maximum amount willing to pay=$1,490,000/2

Maximum amount willing to pay= $745,000

Therefore the maximum amount that Yuri would be willing to pay in order to be fully insured against the risk of losing his ship is $745,000