# Expected Value Decision

Suppose that a car rental agency offers insurance for a week that will cost \$10 per day. A minor fender bender will cost \$1,500, while a major accident might cost \$15,000 in repairs. Without the insurance, you would be personally liable for any damages. What should you do? Clearly, there are two decision alternatives: take the insurance or do not take the insurance. The uncertain consequences, or events that might occur, are that you would not be involved in an accident, that you would be involved in a fender bender, or that you would be involved in a major accident. Assume that you researched insurance industry statistics and found out that the probability of major accident is 0.05%, and that the probability of a fender bender is 0.16%. What is the expected value decision? Would you choose this? Why or why not? What would be some alternate ways to evaluate risk?
The decision to take or not to take an insurance cover is involves evaluation if a risky alternative. The risk of the alternative involves heavy losses because its value may differ from the expected value of the alternative. This paper will use the concept of certainty equivalent to find the best decision that should be adopted by the decision maker. The expected value decision is calculated as follows:
The rental agency insurance offer will cost \$70 per week (\$10*7).
The expected value decision of taking up the insurance offer is as follows:
0.05/100*15,000 + 0.16/100*1,500 + (1-0.05/100-0.16/100)*(-70) = \$-59.95
The expected value decision of not taking up the insurance offer is as follows:
0.05/100*(-15,000) + 0.16/100*(-1,500) + (1-0.05/100-0.16/100)*70 = \$59.95
Decision: I cannot take up the insurance offer because its expected value of decision is less than that of not taking it (Lipton, 1991).
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