For a Markov chain with a discrete or continuous set of states, the problem of finding two Markov stoppings for which difference between the expectation values of the random process in these times has a maximum value is considered. Interpretation of the problem is as follows: the time of purchase and sale of a financial asset at a time when the price of the asset changes according to a Markov chain with given transition probability matrix. The numerical results for a number of models of Markov chains are given.