A representative agent model based on risk-neutral prices

TL;DR

This paper develops a representative agent model based on risk-neutral prices, linking it to eigenpair problems of differential operators, and characterizes all meaningful solutions as a one-parameter family.

Contribution

It introduces a novel method to derive representative agent models from risk-neutral information using eigenpair analysis of differential operators.

Findings

Characterizes all meaningful eigenpairs as a one-parameter family

Provides necessary and sufficient conditions for eigenpair existence

Derives a representative agent model from the eigenpairs

Abstract

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.