On the Existence of Shadow Prices

For utility maximization problems under proportional transaction costs, it hasbeen observed that the original market with transaction costs can sometimes be replacedby 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 toexist. On the other hand, we prove that short selling constraints are a suffcient conditionto warrant their existence, even in very general multi-currency market models with possiblydiscontinuous bid-ask-spreads.[...]