Mr Euler Owns A House Whose Value Is 500 000 It Is Known That The Probability That There Is A Fire And His House Is B 1 (36.94 KiB) Viewed 42 times
Mr. Euler owns a house whose value is $500,000. It is known that the probability that there is a fire and his house is be burnt to ash (→ the value of your house becomes zero) in one year is 0.001 (=1/1,000). He is considering about purchasing an insurance if the condition of the insurance contract is attractive. An agent working for an insurance company InsCo approached to him and offered an insurance contract such that: 1) Mr. Euler pays amount of money $C for the one-year contract, and 2) If there is a fire and Mr. Euler's house is burnt, the company will give him $500,000. Mr. Euler has $100,000 cash in addition to the house, and he does not have any debt. (So his current total asset is $600,000.) Current total asset of the InsCo is $1,000,000,000. a. Draw the decision trees for 1) Mr. Euler and 2) InsCo.
b. If Mr. Euler is risk neutral (= he wants to maximize the expected value of his total asset after one year), what is the upper bound of the contract price ($C) that he would accept? c. If InsCo is risk neutral (= InsCo wants to maximize the expected value of the company's total asset after one year), what is the lower bound of the contract price that the company would accept? d. Suppose that Mr. Euler is making decision based on the following utility function: UE(Ve) = ln(value of Mr. Euler's total asset after one year). What is the upper bound of the contract price that he would accept? e. Suppose that InsCo is making decision based on the following utility function: Uc(Vc) = ln(value of InsCo's total asset after one year). What is the lower bound of the contract price that the company would accept? (Hint: In(1 + x) = x for x < 1.)
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