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Efficient frontier of utility and CVaR

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  • Harry Zheng

Abstract

We study the efficient frontier problem of maximizing the expected utility of terminal wealth and minimizing the conditional VaR of the utility loss. We establish the existence of the optimal solution with the convex duality analysis. We find the optimal value of the constrained problem with the sequential penalty function and the dynamic programming method. Copyright Springer-Verlag 2009

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  • Harry Zheng, 2009. "Efficient frontier of utility and CVaR," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 129-148, August.
    • Handle: RePEc:spr:mathme:v:70:y:2009:i:1:p:129-148
    DOI: 10.1007/s00186-008-0234-9
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    4. Tomasz R. Bielecki & Hanqing Jin & Stanley R. Pliska & Xun Yu Zhou, 2005. "Continuous‐Time Mean‐Variance Portfolio Selection With Bankruptcy Prohibition," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 213-244, April.
    5. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    Cited by:

    1. Bernardo K. Pagnoncelli & Adriana Piazza, 2017. "The optimal harvesting problem under price uncertainty: the risk averse case," Annals of Operations Research, Springer, vol. 258(2), pages 479-502, November.
    2. Li, Jing & Xu, Mingxin, 2009. "Minimizing Conditional Value-at-Risk under Constraint on Expected Value," MPRA Paper 26342, University Library of Munich, Germany, revised 25 Oct 2010.
    3. Nader Trabelsi & Aviral Kumar Tiwari, 2019. "Market-Risk Optimization among the Developed and Emerging Markets with CVaR Measure and Copula Simulation," Risks, MDPI, vol. 7(3), pages 1-20, July.

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