uncertainty

# uncertainty - 1 Examples on choice under uncertainty This...

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1 Examples on choice under uncertainty This note discusses some examples relating to the choice under uncertainty, both for investment and insurance. 1.1 Examples on insurance When dealing with questions related to insurance, we can essentially ask two he or she willing to pay for a given insurance contract. Second, for given terms, how much insurance would an individual be willing to purchase. Note that any preferences (utility function), the likelihood of an accident and the damages in realized wealth is U ( W ) = p W; the probability of an accident is p = 1 4 and the damages in the case of an accident are D = 12 : Further, Tom starts with a wealth of \$16. 1.1.1 How much would you pay? When the question relates to how much Tom would pay for a given insurance, then the solution boils down to comparing two alternatives: choosing to buy the o/ered insurance and choosing not to buy insurance. Let the coverage o/ered be full ( X = 12) and let us ask how much would Tom be willing to pay for this insurance contract (in terms of maximum premium M ). expected utility is Eu no = 1 4 p W + 3 4 p W = 1 4 p 16 12 + 3 4 p 16 = 1 4 2 + 3 4 4 = 14 4 = 3 1 2 The second alternative for Tom is to buy the insurance at a premium M; which yields an expected utility of Eu yes = 1 4 p W + 3 4 p W = 1 4 p 4 + 12 M + 3 4 p 16 M = p 16 M: Tom is willing to buy insurance as long as he is better o/ buying insurance, or Eu yes ± Eu no , p 16 M ± 3 1 2 : Of course, the higher the premium, the worse o/ Tom is, so the maximum he 1

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## This note was uploaded on 04/07/2009 for the course BUAD 351 taught by Professor Eastin during the Spring '07 term at USC.

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uncertainty - 1 Examples on choice under uncertainty This...

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