List and briefly describe the main axioms underlying the expected utility theory. (10 Marks)

Using a fair lottery with two equally probable outcomes, prove that a risk averse investor is characterized by a concave utility function. (20 Marks)

Assume a risk averse investor that is characterized by the logarithmic utility function. The goal of the investor is to maximize the utility of the end-of-period by optimally allocating her wealth between a risky and a risk-free asset. Prove that if the risk premium is zero, the investor will not allocate any of her capital on the risk asset.