# Existence of shadow prices in finite probability spaces

## Author Info

Listed author(s):
• Jan Kallsen

()

• Johannes Muhle-Karbe

()

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## Abstract

A shadow price is a process $${\widetilde{S}}$$ lying within the bid/ask prices $${\underline{S},\overline{S}}$$ of a market with proportional transaction costs, such that maximizing expected utility from consumption in the frictionless market with price process $${\widetilde{S}}$$ leads to the same maximal utility as in the original market with transaction costs. For finite probability spaces, this note provides an elementary proof for the existence of such a shadow price. Copyright Springer-Verlag 2011

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File URL: http://hdl.handle.net/10.1007/s00186-011-0345-6

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## Bibliographic Info

Article provided by Springer & Gesellschaft für Operations Research (GOR) & Nederlands Genootschap voor Besliskunde (NGB) in its journal Mathematical Methods of Operations Research.

Volume (Year): 73 (2011)
Issue (Month): 2 (April)
Pages: 251-262

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 Handle: RePEc:spr:mathme:v:73:y:2011:i:2:p:251-262 DOI: 10.1007/s00186-011-0345-6 Contact details of provider: Web page: http://www.springer.com Web page: http://www.ngb-online.nl/ Order Information: Web: http://www.springer.com/economics/journal/00186

## References

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1. repec:dau:papers:123456789/5630 is not listed on IDEAS
2. Cvitanic, Jaksa & Wang, Hui, 2001. "On optimal terminal wealth under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 223-231, April.
3. Jaksa Cvitanić & Ioannis Karatzas, 1996. "HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH-super-2," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165.
4. J. Kallsen & J. Muhle-Karbe, 2010. "On using shadow prices in portfolio optimization with transaction costs," Papers 1010.4989, arXiv.org.
5. Lamberton, Damien & Pham, Huyên & Schweizer, Martin, 1998. "Local risk-minimization under transaction costs," SFB 373 Discussion Papers 1998,18, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
6. Griselda Deelstra & Huyên Pham & Nizar Touzi, 2001. "Dual formulation of the utility maximisation problem under transaction costs," ULB Institutional Repository 2013/7596, ULB -- Universite Libre de Bruxelles.
7. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48.
8. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
9. Paolo Guasoni & Mikl\'os R\'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
10. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
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