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Maximizing survival, growth and goal reaching under borrowing constraints

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  • Haluk Yener

Abstract

In this paper, we consider the survival, growth and goal reaching maximization problems treated in Browne [ Math. Oper. Res. , 1997, 22 , 468-493] and solve them in a market constrained due to borrowing prohibition. To solve the problems, we first construct an auxiliary market introduced by Cvitanic and Karatzas [ Ann. Appl. Probab. , 1992, 2 , 767-818] and then apply the dynamic programming approach. Via our solutions, an alternative approach is introduced in order to solve the problems defined under an auxiliary market.

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  • Haluk Yener, 2015. "Maximizing survival, growth and goal reaching under borrowing constraints," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 2053-2065, December.
    • Handle: RePEc:taf:quantf:v:15:y:2015:i:12:p:2053-2065
    DOI: 10.1080/14697688.2014.972435
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    1. 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.
    2. Bayraktar, Erhan & Young, Virginia R., 2007. "Minimizing the probability of lifetime ruin under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 196-221, July.
    3. 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.
    4. Cuoco, Domenico & Cvitanic, Jaksa, 1998. "Optimal consumption choices for a 'large' investor," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 401-436, March.
    5. Virginia Young, 2004. "Optimal Investment Strategy to Minimize the Probability of Lifetime Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(4), pages 106-126.
    6. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    7. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    8. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
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    Cited by:

    1. 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.
    2. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.

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