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A Martingale Characterization of Consumption Choices and Hedging Costs with Margin Requirements

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  • Domenico Cuoco
  • Hong Liu
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Abstract

This paper examines optimal consumption and investment choices and the cost of hedging contingent claims in the presence of margin requirements or, more generally, of nonlinear wealth dynamics and constraints on the portfolio policies. Existence of optimal policies is established using martingale and duality techniques under general assumptions on the securities' price process and the investor's preferences. As an illustration, explicit solutions are provided for an agent with 'logarithmic' utility. A PDE characterization of the cost of hedging a nonnegative path-independent European contingent claim is also provided. Copyright Blackwell Publishers Inc. 2000.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Mathematical Finance.

Volume (Year): 10 (2000)
Issue (Month): 3 ()
Pages: 355-385

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Handle: RePEc:bla:mathfi:v:10:y:2000:i:3:p:355-385

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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627

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Cited by:
  1. Long Nguyen-Thanh, 2002. "Consumption and Investment Optimization under Constraints," Finance 0211004, EconWPA, revised 19 Nov 2002.
  2. Thomas Breuer & Martin Janda─Źka, 2008. "Portfolio selection with transaction costs under expected shortfall constraints," Computational Management Science, Springer, vol. 5(4), pages 305-316, October.
  3. Cuoco, Domenico & Liu, Hong, 2006. "An analysis of VaR-based capital requirements," Journal of Financial Intermediation, Elsevier, vol. 15(3), pages 362-394, July.
  4. Long Nguyen-Thanh, 2003. "Investment Optimization under Constraints," Finance 0301005, EconWPA, revised 10 Jan 2003.
  5. Chou, Pin-Huang & Li, Wen-Shen & Zhou, Guofu, 2006. "Portfolio optimization under asset pricing anomalies," Japan and the World Economy, Elsevier, vol. 18(2), pages 121-142, March.
  6. Basak, Suleyman & Croitoru, Benjamin, 2004. "On the Role of Arbitrageurs in Rational Markets," CEPR Discussion Papers 4768, C.E.P.R. Discussion Papers.
  7. Liu, Hong & Yong, Jiongmin, 2005. "Option pricing with an illiquid underlying asset market," Journal of Economic Dynamics and Control, Elsevier, vol. 29(12), pages 2125-2156, December.
  8. Dai, Min & Jin, Hanqing & Liu, Hong, 2011. "Illiquidity, position limits, and optimal investment for mutual funds," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1598-1630, July.
  9. Gibson, Rajna & Murawski, Carsten, 2013. "Margining in derivatives markets and the stability of the banking sector," Journal of Banking & Finance, Elsevier, vol. 37(4), pages 1119-1132.
  10. Frank Milne & Xing Jin, 2006. "Taxation and Transaction Costs in a General Equilibrium Asset Economy," Working Papers 1111, Queen's University, Department of Economics.

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