Dynamic programming with returns in random variables spaces

Abstract

This paper presents a model o f dynamic, discrete decision-making problem (finite number of periods, states and decision variables). Described process has returns in random variables spaces equipped with partial order. The model can be applied for many multi-stage, multi-criteria decision making problems. There are a lot o f order relations to compare random variables. Properties o f those structures let us apply Bellman’s Principle o f dynamic programming. The result o f using this procedure is obtainment o f a whole set o f optimal values (in the sense o f order relation). For illustration, there is presented a numerical example.