Problem 1 Whether the stock goes up tomorrow depends upon whether it increased today and yesterday....

Problem 1

Whether the stock goes up tomorrow depends upon whether it increased today and yesterday. If the stock increased today and yesterday, it will decrease tomorrow with probability α1 . If the stock increased today and decreased yesterday, it will decrease tomorrow with probability α2. If the stock decreased today and increased yesterday, it will decrease tomorrow with probability α3. Finally, if the stock decreased today and yesterday, it will decrease tomorrow with probability α4.

a) Define the states for a Markov chain that represent this system.

b) Construct the (one-step) transition matrix of the Markov chain.

c) Explain why the states used for this Markov chain cause the mathematical definition of the Markovian property to hold even though what happens in the future (tomorrow) depends upon what happened in the past (yesterday) as well as the present (today).

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Expert Solution

orchestra answered 1 year ago

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