  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.
