Q2. (i)Consider a risk averse investor who must decide how much of hisinitial wealth w to put into a risky asset. The risky asset can have any of the positiveor negative rates of return r with probability density function f(r). If ß is the amountof wealth to be put into the risky asset, final wealth under rate of return r will be(w B) + (1+r)ß = w+ ßr. The investor's problem is to choose 3 to maximize theexpected utility of wealth. We can write this formally as the following single-variableoptimization problem(1)Suppose we have interior optimal 3* falls in (0, w), which is determined by the followingfirst order condition:Ju'(w + ßr)rf(r)dr = 0.(2)Define A(w)as a measure of absolute risk aversion. Please show that ifu(.) displays decreasing absolute risk aversion (DARA), i.e. A(w) decreases with w, thenthe risky asset must be a "normal" good, i.e. 3* increases with w. [Hint: Please readExample 2.6 in Jehle and Reny.]max fu(w + Br)f(r)dr s.t.: 0 ≤ B ≤w.Bu" (w)=u' (w)(ii) t. Can you provide one example for such DARA u(.)? Explain why thisu() exhibits DARA.

Decreasing absolute risk aversion represents that when wealth increases the amount invested in risky…

Answered: Q2. (i) Consider a risk averse investor…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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