An investor lives for 2 periods and has the utility function u defined over the final wealth as u (w) = y²c² + B (yE (w) — 1/1²V (w)). The investor is born at t=0 with wealth wo = 2 and wants to choose a portfolio which maximizes her final wealth w₁, which you will recognize is a random variable. There are two assets that the investor can invest in - (i) a bond which pays a sure return 0.01, and (ii) a stock which follows a Normal distribution N (0.02, 0.08). The investor must also eat at time t = 0, and her consumption is Co. The discount rate is given by ß = 0.897, and her risk aversion is given by y = 3.2. Find her optimal consumption which maximizes her utility.
An investor lives for 2 periods and has the utility function u defined over the final wealth as u (w) = y²c² + B (yE (w) — 1/1²V (w)). The investor is born at t=0 with wealth wo = 2 and wants to choose a portfolio which maximizes her final wealth w₁, which you will recognize is a random variable. There are two assets that the investor can invest in - (i) a bond which pays a sure return 0.01, and (ii) a stock which follows a Normal distribution N (0.02, 0.08). The investor must also eat at time t = 0, and her consumption is Co. The discount rate is given by ß = 0.897, and her risk aversion is given by y = 3.2. Find her optimal consumption which maximizes her utility.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:An investor lives for 2 periods and has the utility function u defined over the
final wealth as u (w) = y²c + B (r E (w) – y²V (w)). The investor is
born at t = 0 with wealth wo = 2 and wants to choose a portfolio which
maximizes her final wealth
which you will recognize is a random variable.
י ןUו
There are two assets that the investor can invest in - (i) a bond which pays a sure
return 0.01 , and (ii) a stock which follows a Normal distribution N (0.02,
0.08). The investor must also eat at time t = 0, and her consumption is co.
The discount rate is given by ß = 0.897, and her risk aversion is given by y =
3.2. Find her optimal consumption which maximizes her utility.
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