A Turnpike Theorem For A Risk-Sensitive Markov Decision Process with Stopping

Abstract

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.