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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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    Citations

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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, vol. 81(1), pages 143-173, July.
    2. 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.
    3. 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.
    4. Thomas Breuer & Martin Jandačka, 2008. "Portfolio selection with transaction costs under expected shortfall constraints," Computational Management Science, Springer, vol. 5(4), pages 305-316, October.
    5. 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.
    6. Nguyen-Thanh Long, 2004. "Investment optimization under constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 175-201, October.
    7. 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.
    8. 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.
    9. Cuoco, Domenico & Liu, Hong, 2006. "An analysis of VaR-based capital requirements," Journal of Financial Intermediation, Elsevier, vol. 15(3), pages 362-394, July.
    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.
    11. 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.
    12. 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.
    13. Long Nguyen-Thanh, 2002. "Consumption and Investment Optimization under Constraints," Finance 0211004, EconWPA, revised 25 Mar 2003.

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