Consider an investor whose function of utility over non-negative levels of wealth can be represented as u(w) = ln(w).

A. Is this investor risk loving, risk neutral or risk averse? Provide reasonings of your answer.

B. This investor now decides to put a part of his initial wealth w0 into a risky asset. There are n senarios of possible outcomes, in which the risky asset can have positive or negative rate of return ri with probability pi , i = 1, 2, 3, ..., n. If is the amount of wealth to be invested in the risky asset, calculate this investors Certainty Equivalent CE and Risk Premium P.

C. Assume that this investor knows that when he puts an amount of wealth into the risky asset, this investment (g) will offer 50-50 odds of winning or losing with the rate of return r (that is, r is positive in case of winning and negative in case of losing). Show that CE < E(g) and P > 0.