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Consider the decision problem of investing an amount of wealth W into a risky asset with return 0.1 with probability p R= −0.05with probability 1−p and into a risk-less asset with risk-free interest rate r=2%. You are a risk averse investor with utility function U(WT)=10+ln(WT) where WT is the amount of wealth at the end of the investment. a) Find the optimal allocation in risky and risk-less assets as a function of the probability p and the initial amount of wealth W invested. b) Compute the optimal allocation for a probability value p=0.5. c) What is the lower bound of the probability p for investing a positive share into the risky asset? d) What is the lower bound of p for starting to borrow money at the risk- less interest rate and invest an amount larger than W in the risky asset?
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