  For utility maximization problems under proportional transaction costs, it
has been observed that the original market with transaction costs can sometimes
be replaced by a frictionless "shadow market" that yields the same optimal
strategy and utility. However, the question of whether or not this indeed holds
in generality has remained elusive so far. In this paper we present a
counterexample which shows that shadow prices may fail to exist. On the other
hand, we prove that short selling constraints are a sufficient condition to
warrant their existence, even in very general multi-currency market models with
possibly discontinuous bid-ask-spreads.
