Date Added: May 2011
The discounted utility with a constant discount rate was introduced by Samuelson (1937). Twenty years later Koopmans (1960) characterized axiomatically a class of recursive utilities, which also includes the classical model as a special case. A fairly large number of researchers have used the discounting rule to various sequential decision-making problems, see Blackwell (1965); Stokey et al. (1989); Hern?andez-Lerma and Lasserre (1996) and references therein. A common feature of the aforementioned works is the assumption that the discount factor is constant. This fact significantly simplifies the analysis. Namely, in order to obtain a solution to the Bellman equation, one can directly apply the Banach Contraction Principle, if the immediate return function is bounded.