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CRRA Utility Maximization under Risk Constraints

Author

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

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.

Suggested Citation

  • Santiago Moreno-Bromberg & Traian A. Pirvu & Anthony Réveillac, 2011. "CRRA Utility Maximization under Risk Constraints," SFB 649 Discussion Papers SFB649DP2011-043, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2011-043
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    More about this item

    Keywords

    BSDE; CRRA preferences; constrained utility maximization; correspondences; risk measures;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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