13.2 The price of a certain stock is fluctuating among $10, $20, and $30 from month to month. Market analysis indicates that given that the stock is at $10 in the current month, then in the following month it will be at $10 with probability 0.8 and at $20 with probability 0.2. Similarly, given that the stock is at $20 in the current month, then in the following month it will be at $10 with probability 0.25, at $20 with probability 0.50, and at $30 with probability 0.25. Finally, given that the stock is at $30 in the current month, then in the following month it will be at $20 with probability 0.625 and at $30 with probability 0.375. Given a discount factor of 0.9, use the policy improvement method to determine when to sell and when to hold the stock to maximize the expected long-run total discounted profit.