We offer the quantitative estimation of stability of risk-sensitive cost optimization in the problem of optimal stopping of Markov chain on a Borel space X. It is supposed that the transition probability p(⋅|x), x∈X is approximated by the transition probability p˜(⋅|x), x∈X, and that the stopping rule f˜∗ , which is optimal for the process with the transition probability p˜ is applied to the process with the transition probability p. We give an upper bound (expressed in term of the total variation distance: supx∈X∥p(⋅|x)−p˜(⋅|x)∥) for an additional cost paid for using the rule f˜∗ instead of the (unknown) stopping rule f∗ optimal for p.