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Outperforming A Stochastic Benchmark Under Borrowing And Rectangular Constraints

Author

Listed:
  • Haluk Yener

    (Istanbul Bilgi University)

  • Fuat Can Beylunioglu

    (Istanbul Bilgi University)

Abstract

In this paper, we extend Browne (1999) into the cases of borrowing and rectangular constraints. To address the constraints, we construct an auxiliary market by employing the framework of Cvitanic and Karatzas (1992). Under this framework, we show how problems concerned with survival, growth and goal reaching with respect to a benchmark can be solved by applying the techniques of stochastic optimal control. From the solutions, we see that, while the results under the borrowing constraints may be obtained analytically, the results under the rectangular constraints require a computational procedure. Furthermore, we provide an analysis by using our solutions to see the effect of constraints and changes in key parameters on the optimal results. We also conduct a numerical analysis with three examples to clarify further the effect of the constraints on the investment behaviour of an investor trading in favorable markets.

Suggested Citation

  • Haluk Yener & Fuat Can Beylunioglu, 2017. "Outperforming A Stochastic Benchmark Under Borrowing And Rectangular Constraints," Working Papers 1701, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    • Handle: RePEc:bli:wpaper:1701
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    File URL: https://cefis.bilgi.edu.tr/pdf/CEFIS1701.pdf
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    References listed on IDEAS

    as
    1. Haluk Yener, 2015. "Maximizing survival, growth and goal reaching under borrowing constraints," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 2053-2065, December.
    2. Leonard Maclean & Edward Thorp & William Ziemba, 2010. "Long-term capital growth: the good and bad properties of the Kelly and fractional Kelly capital growth criteria," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 681-687.
    3. Vila, Jean-Luc & Zariphopoulou, Thaleia, 1997. "Optimal Consumption and Portfolio Choice with Borrowing Constraints," Journal of Economic Theory, Elsevier, vol. 77(2), pages 402-431, December.
    4. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    5. Jin, Xing & Zhang, Kun, 2013. "Dynamic optimal portfolio choice in a jump-diffusion model with investment constraints," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1733-1746.
    6. Jér^me Detemple & Marcel Rindisbacher, 2005. "Closed‐Form Solutions For Optimal Portfolio Selection With Stochastic Interest Rate And Investment Constraints," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 539-568, October.
    7. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    8. Wendell H. Fleming & Thaleia Zariphopoulou, 1991. "An Optimal Investment/Consumption Model with Borrowing," Mathematics of Operations Research, INFORMS, vol. 16(4), pages 802-822, November.
    9. Leonard C. MacLean & Edward O. Thorp & Yonggan Zhao & William T. Ziemba, 2011. "Medium Term Simulations of The Full Kelly and Fractional Kelly Investment Strategies," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 38, pages 543-561, World Scientific Publishing Co. Pte. Ltd..
    10. Hua He & Neil D. Pearson, 1991. "Consumption and Portfolio Policies With Incomplete Markets and Short‐Sale Constraints: the Finite‐Dimensional Case1," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 1-10, July.
    11. Stanley R. Pliska, 1986. "A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 371-382, May.
    12. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    13. Sid Browne, 1997. "Survival and Growth with a Liability: Optimal Portfolio Strategies in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 468-493, May.
    14. Tepla, Lucie, 2000. "Optimal portfolio policies with borrowing and shortsale constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1623-1639, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Hamilton-Jacobi-Bellman Equations; Stochastic optimal control; Portfolio selection; Borrowing constraints; Rectangular constraints; Benchmark; Auxiliary Market;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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