Question

1. Consider the following problem $20. If stock 1 is selling for $10 today, there is a .80 chance that it will sell for $10 for tomorrow. If it is selling for $20 today, there is a .90 chance that it will sell for $20 tomorrow Consider two stocks. Stock 1 always sells for $10 or Stock 2 always sells for $10 or $25. If stock 2 sells today for $10 there is a .90 chance that it will sell tomorrow for $10. If it sells today for $25, there is a .85 chance that it will sell tomorrow for $25 Let X denote the price of the 1st stock and Y denote the price of the 2nd stock during the nth day. Assume that {Xn : n > 0} and {Y, : n 20} are discrete time Markov chains (a) What is the long-run distribution of {X n 0}? (b) What is the long-run distribution of {Y n 2 0}? (c) On January 1st, your grand parents decide to give you a gift of 300 shares of either Stock 1 or Stock 2. You are to pick one stock. Once you pick the stock you cannot change your mind. To take advantage of a certain tax law, your grand parents dictate that one share of the chosen stock is sold on each trading day. Which stock should you pick to maximize your gift account by the end of the year? (Explain your answer.)

Answer 1

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