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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.

Suggested Citation

  • 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, July.
    • Handle: RePEc:bla:mathfi:v:10:y:2000:i:3:p:355-385
    DOI: 10.1111/1467-9965.00099
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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. Wei Yan, 2017. "Closed-Form Optimal Strategies of Continuous-Time Options with Stochastic Differential Equations," Complexity, Hindawi, vol. 2017, pages 1-11, July.
    4. 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.
    5. 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.
    6. 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.
    7. Roche, Hervé & Tompaidis, Stathis & Yang, Chunyu, 2013. "Why does junior put all his eggs in one basket? A potential rational explanation for holding concentrated portfolios," Journal of Financial Economics, Elsevier, vol. 109(3), pages 775-796.
    8. 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.
    9. 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.
    10. Rytchkov, Oleg, 2016. "Time-Varying Margin Requirements and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 51(2), pages 655-683, April.
    11. Yuan Zhou & Zhe Wu, 2013. "Mean-Variance Portfolio Selection with Margin Requirements," Journal of Mathematics, Hindawi, vol. 2013, pages 1-9, April.
    12. Ramírez, Hugo E. & Serrano, Rafael, 2025. "Optimal investment with insurable background risk and nonlinear portfolio allocation frictions," Applied Mathematics and Computation, Elsevier, vol. 485(C).
    13. 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.
    14. Cuoco, Domenico & Liu, Hong, 2006. "An analysis of VaR-based capital requirements," Journal of Financial Intermediation, Elsevier, vol. 15(3), pages 362-394, July.
    15. Frank Milne & Xing Jin, 2006. "Taxation And Transaction Costs In A General Equilibrium Asset Economy," Working Paper 1111, Economics Department, Queen's University.
    16. 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.
    17. 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.
    18. Long Nguyen-Thanh, 2002. "Consumption and Investment Optimization under Constraints," Finance 0211004, University Library of Munich, Germany, revised 25 Mar 2003.
    19. Rafael Serrano & Camilo Castillo, 2018. "ALM for insurers with multiple underwriting lines and portfolio constraints: a Lagrangian duality approach," Papers 1810.08466, arXiv.org, revised Aug 2021.
    20. David C. Ling & Yan Lu & Sugata Ray, 2021. "How do Personal Real Estate Transactions Affect Productivity and Risk Taking? Evidence from Professional Asset Managers," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 49(S1), pages 7-40, March.

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