On the existence of shadow prices

Muhle-Karbe, Johannes; Kallsen, Jan; Campi, Luciano; Benedetti, Giuseppe

Muhle-Karbe, Johannes; Kallsen, Jan; Campi, Luciano; Benedetti, Giuseppe (2013), On the existence of shadow prices, Finance and Stochastics, 17, 4, p. 801-818. http://dx.doi.org/10.1007/s00780-012-0201-4

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00645980/fr/

Date

2013

Journal name

Finance and Stochastics

Volume

Number

Publisher

Springer

Pages

801-818

Abstract (EN)

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 {\em 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.

Subjects / Keywords

short selling constraints; shadow prices; Transaction costs

JEL

D23 - Organizational Behavior; Transaction Costs; Property Rights