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Modeling Liquidity Effects In Discrete Time

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  • Umut Çetin
  • L. C. G. Rogers

Abstract

We study optimal portfolio choices for an agent with the aim of maximising utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence of optimal portfolios and that the marginal utility of the optimal terminal wealth serves as a change of measure to turn the marginal price process of the optimal strategy into a martingale. Finally, we illustrate our results numerically in a Cox-Ross-Rubinstein binomial model with liquidity costs and find the reservation ask prices for simple European put options.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Mathematical Finance.

Volume (Year): 17 (2007)
Issue (Month): 1 ()
Pages: 15-29

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Handle: RePEc:bla:mathfi:v:17:y:2007:i:1:p:15-29

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References

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  1. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
  2. Domenico Cuoco & Jaksa Cvitanic, . "Optimal Consumption Choices for a "Large" Investor," Rodney L. White Center for Financial Research Working Papers 04-96, Wharton School Rodney L. White Center for Financial Research.
  3. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84.
  4. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
  5. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
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Cited by:
  1. Terje Lensberg & Klaus Reiner Schenk-Hopp\'e, 2013. "Hedging without sweat: a genetic programming approach," Papers 1305.6762, arXiv.org.
  2. \c{C}a\u{g}\in Ararat & Andreas H. Hamel & Birgit Rudloff, 2014. "Set-valued shortfall and divergence risk measures," Papers 1405.4905, arXiv.org.
  3. Yan Dolinsky & Halil Mete Soner, 2011. "Duality and Convergence for Binomial Markets with Friction," Papers 1106.2095, arXiv.org.
  4. Schied, Alexander & Schoeneborn, Torsten, 2008. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," MPRA Paper 7105, University Library of Munich, Germany.
  5. Jinqiang Yang & Zhaojun Yang, 2012. "Arbitrage-free interval and dynamic hedging in an illiquid market," Quantitative Finance, Taylor & Francis Journals, vol. 13(7), pages 1029-1039, May.
  6. Alexandre Roch, 2011. "Liquidity risk, price impacts and the replication problem," Finance and Stochastics, Springer, vol. 15(3), pages 399-419, September.
  7. Feyzullah Egriboyun & H. Soner, 2010. "Optimal investment strategies with a reallocation constraint," Computational Statistics, Springer, vol. 71(3), pages 551-585, June.
  8. Dylan Possamai & Nizar Touzi & H. Mete Soner, 2012. "Large liquidity expansion of super-hedging costs," Papers 1208.3785, arXiv.org.
  9. Alexandre F. Roch, 2008. "Liquidity Risk, Price Impacts and the Replication Problem," Papers 0812.2440, arXiv.org, revised Dec 2009.

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