In this paper we study a Markov decision process with a non-linear discount function. Our approach is in spirit of the von Neumann-Morgenstern concept and is based on the notion of expectation. First, we define a utility on the space of trajectories of the process in the finite and infinite time...

This paper generalizes the classical discounted utility model introduced by Samuelson by replacing a constant discount rate with a function. The existence of recursive utilities and their constructions are based on Matkowski's extension of the Banach Contraction Principle. The derived utilities...

We consider a discrete time version of the popular optimal dividend payout problem in risk theory. The novel aspect of our approach is that we allow for a risk averse insurer, i.e., instead of maximising the expected discounted dividends until ruin we maximise the expected utility of discounted...