個經題目之應付保險 - 經濟

※ 引述《tomoya0711 (皇上)》之銘言：
: Socrat owns just one ship. The ship is worth $200 million dollars.
: If the ship sinks, Socrat loses $200 million. The probability that
: it will sink is 0.02. Socrates' total wealth including the value of
: the ship is $225 million. He is an expected utility maximizer with
: von Neuman-Morgenstern utility U(W) equal to the square root of W.
: What is the maximum amount that Socrat would be willing to pay in
: order to be fully insured against the risk of losing this ship?
: a.$4 million
: b.$2 million
: c.$3.84 million
: d.$4.82 million
: e.$5.96 million
: 這題我不管怎麼算我答案都會算成a.
: 不過正確答案的e.我怎麼湊都算不出來
: 麻煩版上的高手幫忙解題
: 先謝謝大家了

U(25)=5 with probability 0.02
U(225)=15 with probability 0.98
So E(U)=0.02*5+0.98*15=14.8
→Certainty equivalent = 14.8^2=219.4
→Insuance premium = 225-219.4=5.96

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