The Third Fundamental Theorem of Asset Pricing allows to apply the Second Fundamental Theorem under very mild regularity conditions regarding the process of asset prices. An economic equilibrium exists if and only if the price process is a martingale. Hence, market efficiency at least requires the absence of weak arbitrage opportunities. I show that no weak arbitrage is necessary but not sufficient to establish a situation where asset prices always "fully reflect" a specific set of information beyond the price history. By contrast, completeness is a sufficient and necessary condition for a market to be informationally efficient, i.e., only in that case past and future events turn out to be conditionally independent of the price history  . At the end of the paper I give different characterizations of market efficiency.
The Third Fundamental Theorem of Asset Pricing allows to apply the Second Fundamental Theorem under very mild regularity conditions regarding the process of asset prices. It has been shown that an economic equilibrium exists if and only if the price process is a martingale. Hence, market efficiency at least requires the absence of weak arbitrage , but this is not sufficient to establish a situation where asset prices always "fully reflect" some information beyond the price history. By contrast, completeness is a sufficient and necessary condition for a market to be informationally efficient, i.e., only in that case past and future events turn out to be independent conditional on the price history with respect to the physical measure . At the end of the paper I give different characterizations of market efficiency.
R
An
It has been shown that an
R
opportunities. I show that no weak arbitrage is necessary but
, but this is
R
a specific set of
some
R
conditionally independent of
independent conditional on
A
with respect to the physical measure