Discounting and Risk Neutrality

Abstract

Consider a binary relation on a real vector space of vector-valued discrete-time stochastic processes. If the binary relation satisfies four axioms, then there are unique discount factors such that preferences regarding stochastic processes induce prefences among present value random vectors. Three of the axioms are familiar: weak ordering, continuity, and non-triviality. The fourth axiom is decomposition. Also, if preferences satisfy the four axioms then the following properties are equivalent: the converse of decomposition, the existence of a felicity function on the set of random vectors, and risk neutrality. In this limited sense, discounting implies risk neutrality.