E[65T1] Problem 5 Suppose an asset manager needs to liquidate a large stock position, namely Q shares of stock. The market for this particular stock is not particularly competitive, so that dumping a large position of stock now would price the price downward. To avoid this, the asset manager decides to sell his stock piecemeal, according to the following strategy: he sells a quantity Q/N of stock at every time T}, that the market moves up by $1 (compared to the previous sale, namely Tk_1) for k = 1, ..,N. Suppose that: P(Tk+1 It = mlTo, To = M1 p)\" Every sale of Q stocks results in trading costs of $0. The interest rate is r. The discounted value of the cost of trading at time k is thus: a) Calculate the expected value of the sum of the discounted costs, namely: Ere] = mg as b) Why is this not a good model of stock prices? What would you add to it (no analysis necessary, we'll discuss better models later)? Hint for part (a): observe that, for any 1: 7E 2' , the increment Ti,\" T1, is independent from the increment T+1 T,. (We say that T, has independent increments)