Problem 4 (15pts).

(a) (10pts). An investor considers the possibility of investing in three assets with the following

possible total return: The total return of the three investment options:

Probability Asset 1 Asset 2 Risk-free0.2

0.4

0.4 3.0 5.0 1.1

1.0 0 1.1

0 -2.0 1.1Assume the logarithmic utility function for the investor. Find his optimal allocation of investment according to his utility.

(b) (5pts). Given a solver for Ax = b, where A 2 Rnn and b 2 Rn are inputs and x 2 Rn is

the output. Make use of this solver for part (a) by writing the the pseudo codes