Q2. (i) Consider a risk averse investor who must decide how much of his initial wealth w to put into a risky asset. The risky asset can have any of the positive or negative rates of return r with probability density function f(r). If ß is the amount of wealth to be put into the risky asset, final wealth under rate of return r will be (w − ß) + (1 + r)ß = w+ ßr. The investor's problem is to choose 3 to maximize the expected utility of wealth. We can write this formally as the following single-variable optimization problem max fu(w + Br)f(r)dr s.t.: 0 ≤ ß ≤w. B (1) Suppose we have interior optimal ß* falls in (0, w), which is determined by the following first order condition: fu' (w+Br)rf(r)dr = 0. (2)
Q2. (i) Consider a risk averse investor who must decide how much of his initial wealth w to put into a risky asset. The risky asset can have any of the positive or negative rates of return r with probability density function f(r). If ß is the amount of wealth to be put into the risky asset, final wealth under rate of return r will be (w − ß) + (1 + r)ß = w+ ßr. The investor's problem is to choose 3 to maximize the expected utility of wealth. We can write this formally as the following single-variable optimization problem max fu(w + Br)f(r)dr s.t.: 0 ≤ ß ≤w. B (1) Suppose we have interior optimal ß* falls in (0, w), which is determined by the following first order condition: fu' (w+Br)rf(r)dr = 0. (2)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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