John Smith, owner of Smith Riverside Diner, is trying to decide whether to purch

Question

John Smith, owner of Smith Riverside Diner, is trying to decide whether to purchase an insurance policy to cover flood damage on his diner that is located on the bank of Mohawk river. Rainstorms occur frequently and then Mohawk river may flood the restaurant. John estimates the potential damage from flood in the coming year as:

John is considering three alternatives for dealing with this flood risk:

• John can buy an insurance policy for $16,000 that would cover 100% of any damage losses that occur.

• John can buy an insurance policy for $8,000 that would cover all damage losses in excess of $28,000.

• John can choose to self-insure, in which case he will not have to pay any insurance premium but will pay for any losses that occur.

Part a): Construct a payoff table for this problem

Part b): What decision should be made according to the Conservative Approach?

Part c): What decision should be made according to the Minimax Regret Approach? Show the Regret table to support your answer.

Part d): What decision should be made according to the Expected Value Approach?

Part e): What is the highest amount of money that John should be willing to pay for perfect information/forecast for his flood damage?

Flood Damage No Damage Mild Damage Severe Damage Total Damage Damage Amount in Dollars $0 $15,000 $35,000 $50,000 Probability 0.62 0.22 0.11 0.05

Explanation / Answer

Part A.

Calculation = Cost of Insurance + Damage Cost Paid

Part B. Decesion according to conseravtive approach i.e MaxiMin rule

Out of the Minimum Payoff , Maximum is at -$16000 , therefore the insurance of $16000 which is 100% cover

PART C. MiniMax Regret Approach

Therefor the $16000 insurance is the best option

Part D Expected value approach

Thus John should stick to self Insurance

PART E - COST OF INFORMATION

EVPI = EVwPI-max(EMV)

-5860 - (-9650) = $3790

Action State of Nature $16000 insurance $8000 insurance $0 insurance No damage -16000 -8000 0 Mild Damage -16000 -23000 -15000 Severe Damage -16000 -36000 -35000 Total Damage -16000 -36000 -50000

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