This paper concerns a Markov decision problem with an infinite planning horizon, stationary data, an exponential utility function, and no discounting, but also with the possibility of voluntary or involuntary termination ( stopping). This paper establishes conditions under which the expected utility of the income received by repeated use of a well-chosen stationary control equals the limit, as n becomes large, of the optimal expected utility for the n-period problem. Tests for these (turnpike) conditions are provided, as is a linear program whose optimal solution determines such a control.