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Constrained nonsmooth utility maximization without quadratic inf convolution

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  • Westray, Nicholas
  • Zheng, Harry

Abstract

We address a constrained utility maximization problem in an incomplete market for a utility function defined on the whole real line. We extend current research in two directions, firstly we allow for constraints on the portfolio process. Secondly we prove our results without relying on the technique of quadratic inf convolution, simplifying the proofs in this area.

Suggested Citation

  • Westray, Nicholas & Zheng, Harry, 2009. "Constrained nonsmooth utility maximization without quadratic inf convolution," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1561-1579, May.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:5:p:1561-1579
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    References listed on IDEAS

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    1. B. Bouchard & N. Touzi & A. Zeghal, 2004. "Dual formulation of the utility maximization problem: the case of nonsmooth utility," Papers math/0405290, arXiv.org.
    2. Bruno Bouchard, 2002. "Utility maximization on the real line under proportional transaction costs," Finance and Stochastics, Springer, vol. 6(4), pages 495-516.
    3. Griselda Deelstra & Huyên Pham & Nizar Touzi, 2001. "Dual formulation of the utility maximisation problem under transaction costs," ULB Institutional Repository 2013/7596, ULB -- Universite Libre de Bruxelles.
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    6. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. Sara Biagini & Marco Frittelli, 2005. "Utility maximization in incomplete markets for unbounded processes," Finance and Stochastics, Springer, vol. 9(4), pages 493-517, October.
    8. Frank Oertel & Mark Owen, 2006. "On utility-based super-replication prices of contingent claims with unbounded payoffs," Papers math/0609403, arXiv.org.
    9. Yuri M. Kabanov & Christophe Stricker, 2002. "On the optimal portfolio for the exponential utility maximization: remarks to the six‐author paper," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 125-134, April.
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    Cited by:

    1. Maxim Bichuch & Stephan Sturm, 2014. "Portfolio optimization under convex incentive schemes," Finance and Stochastics, Springer, vol. 18(4), pages 873-915, October.
    2. Frank Seifried, 2010. "Optimal investment with deferred capital gains taxes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 181-199, February.
    3. Nicholas Westray & Harry Zheng, 2010. "Constrained NonSmooth Utility Maximization on the Positive Real Line," Papers 1010.4055, arXiv.org.
    4. Shaolin Ji & Xiaomin Shi, 2016. "Recursive utility optimization with concave coefficients," Papers 1607.00721, arXiv.org.
    5. Maxim Bichuch & Stephan Sturm, 2011. "Portfolio Optimization under Convex Incentive Schemes," Papers 1109.2945, arXiv.org, revised Oct 2013.

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