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Modeling liquidity effects in discrete time

  • Umut Cetin
  • L.C.G. Rogers

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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File URL: http://eprints.lse.ac.uk/2844/
File Function: Open access version.
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Paper provided by London School of Economics and Political Science, LSE Library in its series LSE Research Online Documents on Economics with number 2844.

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Date of creation: Jan 2007
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Publication status: Published in Mathematical Finance, January, 2007, 17(1), pp. 15-29. ISSN: 0960-1627
Handle: RePEc:ehl:lserod:2844
Contact details of provider: Postal: LSE Library Portugal Street London, WC2A 2HD, U.K.
Phone: +44 (020) 7405 7686
Web page: http://www.lse.ac.uk/

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  1. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84.
  2. Domenico Cuoco & Jaksa Cvitanic, . "Optimal Consumption Choices for a "Large" Investor," Rodney L. White Center for Financial Research Working Papers 4-96, Wharton School Rodney L. White Center for Financial Research.
  3. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
  4. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
  5. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
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