A stochastic decision model with vector-valued reward

Abstract

In this note we consider a non-stationary stochastic decision model with vector-valued reward. Based on Pareto-optimality we define the maximal total reward as a set of vector valued total rewards, which have not a successor with respect to the underlying partially order relation. The principle of optimality is derived. Using the well-known von-Neumann-Morgenstern-property we formulate a Bellman-equation, which consists in a system of iterative set relations.

Keywords:

• Multi-objective stochastic decision model
• principle of optimality

AMS 1980 Subject Classifications:

• Primary: 90 B 50
• Secondary: 93 E 20