(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 $150 with a probability of 1/2 or losing $150 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 $300 with a proba- bility of 1/2 or losing $300 with a probability of 1/2. What is the risk premium now? (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 $150 with a probability of 1/2 or losing $150 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 $300 with a proba- bility of 1/2 or losing $300 with a probability of 1/2. What is the risk premium now