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

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  • Domenico Cuoco
  • Hong Liu

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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  • Domenico Cuoco & Hong Liu, 2000. "A Martingale Characterization of Consumption Choices and Hedging Costs with Margin Requirements," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 355-385.
  • Handle: RePEc:bla:mathfi:v:10:y:2000:i:3:p:355-385
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    1. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103 World Scientific Publishing Co. Pte. Ltd..
    2. Freddy Delbaen, 1992. "Representing Martingale Measures When Asset Prices Are Continuous And Bounded," Mathematical Finance, Wiley Blackwell, pages 107-130.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, pages 327-343.
    4. Naik, Vasanttilak, 1993. " Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-1984, December.
    5. Frey, Rüdiger, 1997. "Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility," Discussion Paper Serie B 401, University of Bonn, Germany.
    6. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    7. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B 294, University of Bonn, Germany.
    8. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, pages 279-302.
    9. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(04), pages 589-607, December.
    10. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    11. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
    12. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, pages 117-133.
    13. Huyěn Pham & Nizar Touzi, 1996. "Equilibrium State Prices In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, pages 215-236.
    14. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, pages 73-88.
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    Cited by:

    1. Basak, Suleyman & Croitoru, Benjamin, 2006. "On the role of arbitrageurs in rational markets," Journal of Financial Economics, Elsevier, pages 143-173.
    2. Nguyen-Thanh Long, 2004. "Investment optimization under constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), pages 175-201.
    3. Mauricio Junca & Rafael Serrano, 2014. "Utility maximization in pure-jump models driven by marked point processes and nonlinear wealth dynamics," Papers 1411.1103, arXiv.org, revised Sep 2015.
    4. 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.
    5. Chou, Pin-Huang & Li, Wen-Shen & Zhou, Guofu, 2006. "Portfolio optimization under asset pricing anomalies," Japan and the World Economy, Elsevier, pages 121-142.
    6. Cuoco, Domenico & Liu, Hong, 2006. "An analysis of VaR-based capital requirements," Journal of Financial Intermediation, Elsevier, pages 362-394.
    7. Frank Milne & Xing Jin, 2006. "Taxation and Transaction Costs in a General Equilibrium Asset Economy," Working Papers 1111, Queen's University, Department of Economics.
    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. Chen, Yingshan & Dai, Min & Xu, Jing & Xu, Mingyu, 2015. "Superhedging under ratio constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 250-264.
    11. Long Nguyen-Thanh, 2002. "Consumption and Investment Optimization under Constraints," Finance 0211004, EconWPA, revised 25 Mar 2003.
    12. Thomas Breuer & Martin Jandačka, 2008. "Portfolio selection with transaction costs under expected shortfall constraints," Computational Management Science, Springer, pages 305-316.
    13. Jang, Bong-Gyu & Park, Seyoung, 2016. "Ambiguity and optimal portfolio choice with Value-at-Risk constraint," Finance Research Letters, Elsevier, vol. 18(C), pages 158-176.

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