Stability of Equilibrium Asset Pricing Models: A Necessary and Sufficient Condition

TL;DR

This paper derives an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon models, improving theoretical understanding and offering a practical Monte Carlo computation method.

Contribution

It provides a precise condition for equilibrium asset prices and links it to stochastic discount factor decompositions, advancing both theory and computational techniques.

Findings

The condition sharpens previous results on asset price equilibrium.

A Monte Carlo method for computing the test value is proposed.

The condition applies to infinite horizon, discrete-time, arbitrage-free models.

Abstract

We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition sharpens and improves on previous results. We connect the condition, and hence the problem of existence and uniqueness of asset prices, with the recent literature on stochastic discount factor decompositions. Finally, we discuss computation of the test value associated with our condition, providing a Monte Carlo method that is naturally parallelizable.