Question: (a) Certainty Equivalent and Risk Premium An investor whose initial wealth is $1, 000 is offered an opportunity to play a fair game with 2

(a) Certainty Equivalent and Risk Premium An investor whose initial wealth is $1, 000 is offered an opportunity to play a fair game with 2 possible outcomes: winning $200 with a probability of 1/2 or losing $200 with a probability of 1/2. The investor utility function is the natural logarithm of his wealth, u(W) = ln(W).

What is the Certainty equivalent of this risky game?

What is the exact risk premium of this risky game?

How good is the approximation obtained by using a Taylor series expansion?

(b) Sensitivity to initial wealth Assume that the initial wealth is $2, 000. What is the risk premium now?

(c) Sensitivity to volatility Assume that the initial wealth is $1, 000 and the outcomes are winning $500 with a probability of 1/2 or losing $500 with a probability of 1/2. What is the risk premium now?

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