A Markovian Stock

Probability Level 2

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?

\frac{4}{5}

\frac{2}{3}

\frac{3}{4}

\frac{5}{6}

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Gabe Smith
Dec 21, 2016

In the steady state, the following equations must be satisfied:

$0.8p + 0.4(1-p) = p$ $0.6(1-p) + 0.2p = 1-p$

Solving these equations gives $p=\frac{2}{3}.$

A Markovian Stock

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