Question

Consider a logarithmic investor (u(z) = lnz) who can invest in a risk-free asset with gross return R and in a risky asset whose gross return is either a with probability (0,1), or b with probability 1. Suppose that 0 < a < R < b and the initial wealth is w. 1. Derive the optimal demand for the risky asset.

2. Examine the eect of change in wealth w on the optimal demand for the risky asset.

3. Examine the eect of an increase of the risk free rate on the optimal demand for the risky asset.

4. Consider an increase in b combined with a reduction of a that leaves a + (1)b unchanged, what is the eect on the optimal demand for the risky asset.