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CRRA Utility Maximization under Risk Constraints

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  • Santiago Moreno-Bromberg
  • Traian Pirvu
  • Anthony R'eveillac

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. the prices of financial assets are modeled by It\^o processes. The dynamic risk constraints, which are time and state dependent, are generated by risk measures. Optimal trading strategies are characterized by a quadratic BSDE. Within the class of \textit{time consistent distortion risk measures}, a three-fund separation result is established. Numerical results emphasize the effects of imposing risk constraints on trading.

Suggested Citation

  • Santiago Moreno-Bromberg & Traian Pirvu & Anthony R'eveillac, 2011. "CRRA Utility Maximization under Risk Constraints," Papers 1106.1702, arXiv.org, revised Mar 2012.
  • Handle: RePEc:arx:papers:1106.1702
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    File URL: http://arxiv.org/pdf/1106.1702
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    References listed on IDEAS

    as
    1. 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.
    2. Leippold, Markus & Trojani, Fabio & Vanini, Paolo, 2006. "Equilibrium impact of value-at-risk regulation," Journal of Economic Dynamics and Control, Elsevier, vol. 30(8), pages 1277-1313, August.
    3. Arjan Berkelaar & Phornchanok Cumperayot & Roy Kouwenberg, 2002. "The Effect of VaR Based Risk Management on Asset Prices and the Volatility Smile," European Financial Management, European Financial Management Association, vol. 8(2), pages 139-164.
    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.
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    Cited by:

    1. Soriano-Morales, Yazmín Viridiana & Vallejo-Jiménez, Benjamín & Venegas-Martínez, Francisco, 2017. "Impact of the Degree of Relative Risk Aversion, the Interest Rate and the Exchange Rate Depreciation on Economic Welfare in a Small Open Economy," MPRA Paper 76441, University Library of Munich, Germany.

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