**Abstract:**

In a financial market composed of $n$ risky assets and a riskless asset,
where short sales are allowed and mean-variance investors can be ambiguity averse, i.e.,
diffident about mean return estimates where confidence
is represented using ellipsoidal uncertainty sets, we derive a closed form
portfolio rule based on a worst case max-min criterion.
Then, in a market where all investors are ambiguity-averse
mean-variance investors with access to given mean return and variance-covariance estimates,
we investigate conditions regarding the existence of an equilibrium price system.
In addition to the usual equilibrium properties that continue to hold in our case,
we show that the diffidence of investors in a homogeneously diffident (with bounded diffidence)
mean-variance investors' market may have a deflationary effect on equilibrium
prices with respect to a pure mean-variance
investors' market.
Deflationary pressure on prices may also occur if one of the investors (in an ambiguity-neutral market)
with no initial short position decides to adopt an ambiguity-averse attitude.
We also establish a CAPM-like property that reduces to the classical CAPM in case all
investors are ambiguity-neutral.
Keywords: Robust optimization, mean-variance portfolio theory, ellipsoidal uncertainty, equilibrium price system.