Time-inconsistent Risk-sensitive Equilibrium for Countable-stated Markov Decision Processes

Abstract

This paper is devoted to solving a time-inconsistent risk-sensitive control problem with parameter ε and its limit case (ε → 0 + ) for countable-stated Markov decision processes (MDPs for short). Since the cost functional is time-inconsistent, it is impossible to find a global optimal strategy for both cases. Instead, for each case, we will prove the existence of time-inconstant equilibrium strategies which verify the so-called step-optimality. Moreover, we prove the convergence of ε-equilibriums and the corresponding value functions as ε → 0 + .