3. Consider a stock that pays dividends of a fraction & of the stock price at discrete times T, T2, T3,..., then the stock price at time t is given by St= (1-6)n[t] Soet+oWt, where n[t] is the number of dividends paid by time t. Suppose that the dividends are re-invested in the stock, then the tradable will be the portfolio of the stock and the reinvested dividends, Zt = (1-6)-n[t] St. (a) Find a measure Q which makes the discounted Z, a martingale. (b) Find the fair price of the stock at time T. (c) Find the price of a forward contract on the stock.