We consider a switching model for a Markov chain xt with a transition probability p(x|B). The goal of a controller is to maximize the average gain by selecting a sequence of stopping times, in which the controller gets rewards and pays costs (depending on xt) in an alternating order. We suppose that the exact transition probability function of the original “real” chain xt is not available to the controller, and he/she is forced to rely on a given approximation &ptilde; to the unknown p. The controller finds a switching policy π optimal for the Markov chain with the transition probability &ptilde;, with a view toπ to the original Markov chain xt. Under certain restrictions on p we give an upper bound for the difference between the maximal gain attainable in switching of xt, and the gain made under the policy π in the original model. The bound is expressed in terms of the total variation distance supx Var (p(x|·), &ptilde;(x|·)).
