On the Existence of Shadow Prices

Details On the Existence of Shadow Prices On the Existence of Shadow Prices

2011-11-28

arxiv.org/abs/1111.6633v1

Economy

Quantitative Finance

Portfolio Management

14 pages, 1 figure

Scientific paper

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.

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