Discounting and Risk Neutrality

Let be a binary relation in which is a real vector space of vector-valued discrete-time Ð ¤ ß Z Ñ Z stochastic processes with as the sequence of zero vectors. If satisfies four axioms, then ! Ð ¤ ß Z Ñ 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 implies where is decomposition \  ] ¤ Ð £ Ñ \ ¤ Ð £ Ñ ] ! ! the sequence of zero vectors. 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.