A Markovian Stock

Over time, you have found that a certain asset seems to follow a Markov model in which it will increase or decrease minute-to-minute according to the model above. For example, if its value increases one minute, it is 80% likely to increase again in the next minute. In the long run, in what percentage of minutes does the stock increase?

Hint: If it increases with probability \(p,\) it decreases with probability \(1-p.\) What value of \(p\) would provide a steady state in this chain?

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