IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1602.00570.html
   My bibliography  Save this paper

Portfolio optimization under dynamic risk constraints: continuous vs. discrete time trading

Author

Listed:
  • Imke Redeker
  • Ralf Wunderlich

Abstract

We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk measure. For continuous- and discrete-time financial markets we investigate the loss in expected utility of intermediate consumption and terminal wealth caused by imposing a dynamic risk constraint. We derive the dynamic programming equations for the resulting stochastic optimal control problems and solve them numerically. Our numerical results indicate that the loss of portfolio performance is not too large while the risk is notably reduced. We then investigate time discretization effects and find that the loss of portfolio performance resulting from imposing a risk constraint is typically bigger than the loss resulting from infrequent trading.

Suggested Citation

  • Imke Redeker & Ralf Wunderlich, 2016. "Portfolio optimization under dynamic risk constraints: continuous vs. discrete time trading," Papers 1602.00570, arXiv.org, revised Aug 2017.
    • Handle: RePEc:arx:papers:1602.00570
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1602.00570
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sofiane Aboura, 2014. "When the U.S. Stock Market Becomes Extreme?," Risks, MDPI, vol. 2(2), pages 1-15, May.
    2. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    3. Christina Büsing & Sigrid Knust & Xuan Thanh Le, 2018. "Trade-off between robustness and cost for a storage loading problem: rule-based scenario generation," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 339-365, December.
    4. Winter, Peter, 2007. "Managerial Risk Accounting and Control – A German perspective," MPRA Paper 8185, University Library of Munich, Germany.
    5. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    6. Jiang Cheng & Hung-Gay Fung & Tzu-Ting Lin & Min-Ming Wen, 2024. "CEO optimism and the use of credit default swaps: evidence from the US life insurance industry," Review of Quantitative Finance and Accounting, Springer, vol. 63(1), pages 169-194, July.
    7. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2014. "Beyond cash-additive risk measures: when changing the numéraire fails," Finance and Stochastics, Springer, vol. 18(1), pages 145-173, January.
    8. Li, Xiao-Ming & Rose, Lawrence C., 2009. "The tail risk of emerging stock markets," Emerging Markets Review, Elsevier, vol. 10(4), pages 242-256, December.
    9. Choo, Weihao & de Jong, Piet, 2015. "The tradeoff insurance premium as a two-sided generalisation of the distortion premium," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 238-246.
    10. Louis Anthony (Tony)Cox, 2008. "What's Wrong with Risk Matrices?," Risk Analysis, John Wiley & Sons, vol. 28(2), pages 497-512, April.
    11. Jay Cao & Jacky Chen & John Hull & Zissis Poulos, 2021. "Deep Hedging of Derivatives Using Reinforcement Learning," Papers 2103.16409, arXiv.org.
    12. Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2019. "Dynamic risk measures for processes via backward stochastic differential equations," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 43-50.
    13. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    14. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    15. Rostagno, Luciano Martin, 2005. "Empirical tests of parametric and non-parametric Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) measures for the Brazilian stock market index," ISU General Staff Papers 2005010108000021878, Iowa State University, Department of Economics.
    16. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    17. Dimitrios G. Konstantinides & Georgios C. Zachos, 2019. "Exhibiting Abnormal Returns Under a Risk Averse Strategy," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 551-566, June.
    18. Pauline Barrieu & Henri Loubergé, 2009. "Hybrid Cat Bonds," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 547-578, September.
    19. Parrini, Alessandro, 2013. "Importance Sampling for Portfolio Credit Risk in Factor Copula Models," MPRA Paper 103745, University Library of Munich, Germany.
    20. Makam, Vaishno Devi & Millossovich, Pietro & Tsanakas, Andreas, 2021. "Sensitivity analysis with χ2-divergences," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 372-383.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1602.00570. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.