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Modeling Liquidity Effects In Discrete Time

  • Umut Çetin
  • 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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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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  1. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
  2. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84.
  3. 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.
  4. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
  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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