Problem 2 Let N1(t) and N2 (73) be two independent Poisson processes with parameters A1 and A2. Suppose that the value of two stocks X105) and X2 (15) each follows a compensated Poisson process: X1(t) : X1(0)+N1(t)A1t X2(t) : X2(0)+N2(t)A2t A portfolio is made up of an shares of stock 1 and \"02 shares of stock 2. The value of the portfolio is denoted by X (t) The arithmetic return r(t, t + At) of the portfolio is denoted by: X(t+A) X(t) 1"(13, t + At) = X(t) Calculate: a) the mean value of the portfolio, i.e., E[X(t)] b) the variance of the value of the portfolio c) the conditional variance of the portfolio return at time t, i.e., Var[r(t, t + A15)|X(t)] d) Is X a martingale? Justify. e) Why is it a bad nancial model