expected value of costs

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 Tk that the market moves up by $1 (compared to the previous sale, namely Tk-1) for k = 1, .., N. Suppose that: m- P(Tk+1 Tk = m|To, ..., Tx) = P(1 p)-1 Every sale of Q stocks results in trading costs of $c. The interest rate is r. The discounted value of the cost of trading at time k is thus: Ch = ce-rT* a) Calculate the expected value of the sum of the discounted costs, namely: N E[C] = El Ch] k=1 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 Tk that the market moves up by $1 (compared to the previous sale, namely Tk-1) for k = 1, .., N. Suppose that: m- P(Tk+1 Tk = m|To, ..., Tx) = P(1 p)-1 Every sale of Q stocks results in trading costs of $c. The interest rate is r. The discounted value of the cost of trading at time k is thus: Ch = ce-rT* a) Calculate the expected value of the sum of the discounted costs, namely: N E[C] = El Ch] k=1