Your wealth at the begining of the period under consideration is $100. You have an opportunity...

 

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Your wealth at the begining of the period under consideration is $100. You have an opportunity to invest Sz in a risky asset, 0 < 100. There is a probability p that the rate of return on the asset will be 0.2 (in which case investing Sr yields back $1.2 x at the end of the period) and a probability 1-p that the rate of return will be -0.1 (in which case investing $a yields back $0.9 2). You are an expected utility maximizer. Your utility function is u(y) = ln(y). where y denotes your wealth at the end of the period. (a) What is the minimal value of the probability p for which your optimal investment is positive? (b) Derive the formula describing how your optimal investment " varies with p. (c) If your wealth increases, does your optimal investment * increase? Explain. Your wealth at the begining of the period under consideration is $100. You have an opportunity to invest Sz in a risky asset, 0 < 100. There is a probability p that the rate of return on the asset will be 0.2 (in which case investing Sr yields back $1.2 x at the end of the period) and a probability 1-p that the rate of return will be -0.1 (in which case investing $a yields back $0.9 2). You are an expected utility maximizer. Your utility function is u(y) = ln(y). where y denotes your wealth at the end of the period. (a) What is the minimal value of the probability p for which your optimal investment is positive? (b) Derive the formula describing how your optimal investment " varies with p. (c) If your wealth increases, does your optimal investment * increase? Explain.