Consider an investor with current wealth Y0 =100 and CRRA utility-of-money function: U(Y) = 1 1 , with =2. The investor has two investment possibilities: a risk-free asset with 3% return and a risky asset. The risky asset pays 2% return with probability 0.4 and 10% return with probability 0.6.

A. Consider the portfolio allocation problem of the investor. Write down the utility maximization problem if she invests a to the risky asset. (15 points)

B. Compute the optimal amount invested in the risky asset. (20 points)