To solve the problem, it is convenient at this stage to impose a continuous approximation to the actual problem: we suppose that the investor can buy and sell fractional shares of stock so that all real values of \(a\) between the constrained bounds in Exercise 13 are possible. This could be the case if one was able to work through a consortium of investors that allows joint ownership of a share of stock. Use Mathematica to simplify the expression inside the DP equation for \(V_{2}\) in terms of \(V_{3}\). What action leads to the maximum? Find \(V_{2}\). Continue to find \(V_{1}, V_{0}\), and the optimal policy. Given the nature of the problem parameters, is the optimal policy intuitively obvious?