On using shadow prices in portfolio optimization with transaction costs
AbstractIn frictionless markets, utility maximization problems are typically solved either by stochastic control or by martingale methods. Beginning with the seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676--713], stochastic control theory has also been used to solve various problems of this type in the presence of proportional transaction costs. Martingale methods, on the other hand, have so far only been used to derive general structural results. These apply the duality theory for frictionless markets typically to a fictitious shadow price process lying within the bid-ask bounds of the real price process. In this paper, we show that this dual approach can actually be used for both deriving a candidate solution and verification in Merton's problem with logarithmic utility and proportional transaction costs. In particular, we determine the shadow price process.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1010.4989.
Date of creation: Oct 2010
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Publication status: Published in Annals of Applied Probability 2010, Vol. 20, No. 4, 1341-1358
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Web page: http://arxiv.org/
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- NEP-ALL-2010-11-06 (All new papers)
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- Stefan Gerhold & Johannes Muhle-Karbe & Walter Schachermayer, 2010. "The dual optimizer for the growth-optimal portfolio under transaction costs," Papers 1005.5105, arXiv.org, revised Oct 2010.
- S\"oren Christensen & Marc Wittlinger, 2012. "Optimal relaxed portfolio strategies for growth rate maximization problems with transaction costs," Papers 1209.0305, arXiv.org.
- Christian Bayer & Bezirgen Veliyev, 2012. "Utility Maximization in a Binomial Model with transaction costs: a Duality Approach Based on the Shadow Price Process," Papers 1209.5175, arXiv.org.
- Jan Kallsen & Johannes Muhle-Karbe, 2012. "Option Pricing and Hedging with Small Transaction Costs," Papers 1209.2555, arXiv.org, revised Dec 2012.
- Jin Hyuk Choi & Mihai Sirbu & Gordan Zitkovic, 2012. "Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs," Papers 1204.0305, arXiv.org, revised Jun 2012.
- Johannes Muhle-Karbe & Ren Liu, 2012. "Portfolio Selection with Small Transaction Costs and Binding Portfolio Constraints," Papers 1205.4588, arXiv.org, revised Jan 2013.
- Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org.
- Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2011. "Transaction Costs, Trading Volume, and the Liquidity Premium," Papers 1108.1167, arXiv.org, revised Jan 2013.
- Dmitry B. Rokhlin, 2011. "On the game interpretation of a shadow price process in utility maximization problems under transaction costs," Papers 1112.2406, arXiv.org, revised Dec 2011.
- Irene Klein & Emmanuel Lepinette & Lavinia Ostafe, 2012. "Large Financial Markets and Asymptotic Arbitrage with Small Transaction Costs," Papers 1211.0443, arXiv.org.
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