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Question An investor can invest in two assets, A and B: A B expected return 6% 3% variance 4% % 25%% The correlation coefficient of the rate of return of the two assets is denoted by p and is assumed to take the value 0.5. The investor is assumed to have an expected utility function of the form: EQ(U ) = E(rp) - Var(5) where o is a positive constant and r, is the rate of return on the assets held by the investor. (i) Determine, as a function of o. the portfolio that maximises the investor's expected utility. [8] (ii) Show that, as of increases, the investor selects an increasing proportion of Asset A. [1] [Total 9](i) What is meant by saying that the process {} } is a martingale with respect to another process {X,}? [2] Let B, (1 2 0 ) be a standard Brownian motion. (ii) Show that B, and B, + kr are both martingales with respect to B , for a suitably chosen value of the constant k , which you should specify. [6] (iii) Show that there is a value of the constant c, which you should specify, such that (a+ bB, ) + or is a martingale with respect to B, , where a and b are constants. [4] [Total 12]