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...

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 4/5 and at $20 with probability 1/5. Similarly, given that the stock is at $20 in the current month, then in the following month it will be at $10 with probability 1/4, at $20 with probability 1/2, and at $30 with probability 1/4. Finally, given that the stock is at $30 in the current month, then in the following month it will be at $20 with probability 5/8 and at $30 with probability 3/8. 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.