  In this paper, we determine a representative agent model based on
risk-neutral information. The main idea is that the pricing kernel is
transition independent, which is supported by the well-known capital asset
pricing theory. Determining the representative agent model is closely related
to the eigenpair problem of a second-order differential operator. The purpose
of this paper is to find all such eigenpairs which are financially or
economically meaningful. We provide a necessary and sufficient condition for
the existence of such pairs, and prove that that all the possible eignepairs
can be expressed as a one-parameter family. Finally, we find a representative
agent model derived from the eigenpairs.
