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CRRA Utility Maximization under Risk Constraints

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  • Santiago Moreno-Bromberg
  • Traian A. Pirvu
  • Anthony Réveillac
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    Abstract

    This paper studies the problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies. The market model considered is continuous in time and incomplete; furthermore, financial assets are modeled by Itô processes. The dynamic risk constraints (time, state dependent) are generated by risk measures. The optimal trading strategy is characterized by a quadratic BSDE. Special risk measures (Value-at-Risk, Tail Value-at-Risk and Limited Expected Loss ) are considered and a three-fund separation result is established in these cases. Numerical results emphasize the effect of imposing risk constraints on trading.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2011-043.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2011-043.

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    Length: 26 pages
    Date of creation: Jul 2011
    Date of revision:
    Handle: RePEc:hum:wpaper:sfb649dp2011-043

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    Related research

    Keywords: BSDE; CRRA preferences; constrained utility maximization; correspondences; risk measures;

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    References

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    1. Juliane Scheffel, 2011. "Identifying the Effect of Temporal Work Flexibility on Parental Time with Children," SFB 649 Discussion Papers SFB649DP2011-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Mechtenberg, Lydia & Münster, Johannes, 2010. "A strategic mediator who is biased into the same direction as the expert can improve information transmission," Discussion Papers, Research Unit: Market Behavior SP II 2010-19, Social Science Research Center Berlin (WZB).
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    4. Wolfgang Karl Härdle & Brenda López Cabrera & Ostap Okhrin & Weining Wang, 2011. "Localising temperature risk," SFB 649 Discussion Papers SFB649DP2011-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Akdeniz Duran, Esra & Härdle, Wolfgang Karl & Osipenko, Maria, 2012. "Difference based ridge and Liu type estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 164-175.
    6. Beresford, Alastair R. & Kübler, Dorothea & Preibusch, Sören, 2010. "Unwillingness to pay for privacy: A field experiment," Discussion Papers, Research Unit: Market Behavior SP II 2010-03, Social Science Research Center Berlin (WZB).
    7. Heike Belitz & Marius Clemens & Christian von Hirschhausen & Jens Schmidt-Ehmcke & Axel Werwatz & Petra Zloczysti, 2011. "An Indicator for National Systems of Innovation - Methodology and Application to 17 Industrialized Countries," SFB 649 Discussion Papers SFB649DP2011-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Shuzhuan Zheng & Lijian Yang & Wolfgang Karl Härdle, 2011. "A Confidence Corridor for Sparse Longitudinal Data Curves," SFB 649 Discussion Papers SFB649DP2011-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Johanna Kappus & Markus Reiß, 2011. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers SFB649DP2011-027, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Wolfgang Karl Härdle & Maria Osipenko, 2011. "Spatial Risk Premium on Weather Derivatives and Hedging Weather Exposure in Electricity," SFB 649 Discussion Papers SFB649DP2011-013, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Wolfgang Karl Härdle & Vladimir Spokoiny & Weining Wang, 2011. "Local Quantile Regression," SFB 649 Discussion Papers SFB649DP2011-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Lu Lin & Feng Li & Lixing Zhu & Wolfgang Karl Härdle, 2011. "Mean Volatility Regressions," SFB 649 Discussion Papers SFB649DP2011-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Strohsal, Till & Weber, Enzo, 2010. "Mean-Variance Cointegration and the Expectations Hypothesis," University of Regensburg Working Papers in Business, Economics and Management Information Systems 442, University of Regensburg, Department of Economics.
    14. Juliane Scheffel, 2011. "How do Unusual Working Schedules Affect Social Life?," SFB 649 Discussion Papers SFB649DP2011-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    15. Markus Reiß & Yves Rozenholc & Charles A. Cuenod, 2011. "Pointwise adaptive estimation for quantile regression," SFB 649 Discussion Papers SFB649DP2011-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Sigbert Klinke, 2011. "Developing web-based tools for the teaching of statistics: Our Wikis and the German Wikipedia," SFB 649 Discussion Papers SFB649DP2011-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    17. Alexander Meyer-Gohde, 2011. "Sticky Information and Determinacy," SFB 649 Discussion Papers SFB649DP2011-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    18. Dirk Hofmann & Salmai Qari, 2011. "The Law of Attraction: Bilateral Search and Horizontal Heterogeneity," SFB 649 Discussion Papers SFB649DP2011-017, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    19. Xiaoliang Liu & Wei Xu & Martin Odening, 2011. "Can crop yield risk be globally diversified?," SFB 649 Discussion Papers SFB649DP2011-018, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    20. Rong Liu & Lijian Yang & Wolfgang K. H�rdle, 2013. "Oracally Efficient Two-Step Estimation of Generalized Additive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 619-631, June.
    21. Markus Reiß, 2011. "Asymptotic equivalence and sufficiency for volatility estimation under microstructure noise," SFB 649 Discussion Papers SFB649DP2011-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    22. Esra Akdeniz Duran & Mengmeng Guo & Wolfgang Karl Härdle, 2011. "A Confidence Corridor for Expectile Functions," SFB 649 Discussion Papers SFB649DP2011-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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