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CRRA utility maximization under risk constraints

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

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

  • Moreno-Bromberg, Santiago & Pirvu, Traian A. & Réveillac, Anthony, 2011. "CRRA utility maximization under risk constraints," SFB 649 Discussion Papers 2011-043, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2011-043
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    References listed on IDEAS

    as
    1. Traian A. Pirvu, 2007. "Portfolio optimization under the Value-at-Risk constraint," Quantitative Finance, Taylor & Francis Journals, vol. 7(2), pages 125-136.
    2. Marcel Nutz, 2009. "The Opportunity Process for Optimal Consumption and Investment with Power Utility," Papers 0912.1879, arXiv.org, revised Jun 2010.
    3. Yiu, K. F. C., 2004. "Optimal portfolios under a value-at-risk constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1317-1334, April.
    4. Bender, Christian & Denk, Robert, 2007. "A forward scheme for backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1793-1812, December.
    5. Gundel, Anne & Weber, Stefan, 2007. "Robust utility maximization with limited downside risk in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1663-1688, November.
    6. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    7. Susanne Emmer & Claudia Klüppelberg & Ralf Korn, 2001. "Optimal Portfolios with Bounded Capital at Risk," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 365-384, October.
    8. Traian A. Pirvu & Gordan Žitković, 2009. "Maximizing The Growth Rate Under Risk Constraints," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 423-455, July.
    9. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    10. Imkeller, Peter & Dos Reis, Gonçalo, 2010. "Path regularity and explicit convergence rate for BSDE with truncated quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 348-379, March.
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    JEL classification:

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

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