Investor A has an initial wealth of $100 and a utility function of the form: U(w) = log(w) where w is her wealth at any time. Investment Z offers her a return of −18% or +20% with equal probability. i. What is her expected utility if she invests nothing in Investment Z? ii. What is her expected utility if she invests entirely in Investment Z? iii. What proportion a of her wealth should she invest in Investment Z to maximize her expected utility? What is her expected utility if she invests this proportion in Investment Z?

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