Sequences of contractions and random fixed point theorems in dynamic programming

Abstract

In this paper we consider a non-stationary discounted dynamic programming model with a random parameter. We associate with this model a backward sequence of decision problems with increasing planning horizon, and study the asymptotic behaviour of optimal rewards. In this analysis we use some results on multifunctions and sequences of contractions, and apply a random analogue of the Banach fixed point theorem. Similar problems were investigated by Qapar [3], and we generalize his results.