State the expected utility theorem and the characteristic of non-satiation.

Let U(w) denote an investor's utility function, where w denotes the investor's level of wealth. (i) In terms of the derivatives of U(w), state the condition for: (a) absolute risk aversion (b) relative risk aversion [1] (ii) Show, for each of the utility functions listed below, whether they display increasing, decreasing, or constant relative and absolute risk aversion. (a) U(w) = 1 -e-aw where a > 0 (b) U(w): -1 where y e (0, 1) [4] Y iii) State with reasons the most suitable characteristic (in terms of absolute risk aversion) of a utility function for a typical investor. [2](i) State the assumptions underlying Mean Variance Portfolio Theory. [2] (ii) Let A and B be two assets with volatility of returns of and of respectively. The coefficient of correlation between the returns of A and B is denoted by p. Derive an expression for the proportion of the asset A held in the minimum variance portfolio comprising only the assets A and B. [2] (iii) Show that the condition for non negative holdings of A and B is p