Kindly help me address this question

Consider a non-dividend-paying security with price S, at time f. The security price follows the stochastic differential equation: dS, = Squat + odZ,) where: Z, is a standard Brownian motion = 16% per annum 0 = 25% per annum / is the time from now measured in years So = 1 (i) Derive the distribution of S. [4] An investor has taken out a house loan, with a repayment of $100,000 due in six years' time. (ii) Determine the amount that the investor would need to invest in the security to give a 75% probability of having an investment value of at least (100,000 in six years' time. [4] The investor only has $50,000 available, which he invests in this security at time 1=0. (iii) Calculate the following risk measures applied to the difference between the value of the security and (100,000 at time / - 6: (a) 90% Value at Risk relative to f100,000 (b ) expected shortfall or surplus relative to f.100,000) [5] (iv) Comment on the implications for the investor of your answers to part (iii). [2] (V) Suggest two changes that the investor might therefore make to his portfolio. [2] ['Total 17]