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The Stability of the Constrained Utility Maximization Problem - A BSDE Approach

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  • Markus Mocha
  • Nicholas Westray
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    Abstract

    This article studies the sensitivity of the power utility maximization problem with respect to the investor's relative risk aversion, the statistical probability measure, the investment constraints and the market price of risk. We extend previous descriptions of the dual domain then exploit the link between the constrained utility maximization problem and continuous semimartingale quadratic BSDEs to reduce questions on sensitivity to results on stability for such equations. This then allows us to prove appropriate convergence of the primal and dual optimizers in the semimartingale topology.

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    File URL: http://arxiv.org/pdf/1107.0190
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1107.0190.

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    Date of creation: Jul 2011
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    Handle: RePEc:arx:papers:1107.0190

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    1. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
    2. Elyès Jouini & Clotilde Napp, 2004. "Convergence of utility functions and convergence of optimal strategies," Finance and Stochastics, Springer, vol. 8(1), pages 133-144, January.
    3. Marcel Nutz, 2009. "The Opportunity Process for Optimal Consumption and Investment with Power Utility," Papers 0912.1879, arXiv.org, revised Jun 2010.
    4. Bruno Bouchard & Huyên Pham, 2004. "Wealth-path dependent utility maximization in incomplete markets," Finance and Stochastics, Springer, vol. 8(4), pages 579-603, November.
    5. Marie-Amélie Morlais, 2009. "Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem," Finance and Stochastics, Springer, vol. 13(1), pages 121-150, January.
    6. Napp, Clotilde & Jouini, Elyès, 2004. "Convergence of utility functions and convergence of optimal strategies," Economics Papers from University Paris Dauphine 123456789/355, Paris Dauphine University.
    7. Kasper Larsen, 2009. "Continuity Of Utility-Maximization With Respect To Preferences," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 19(2), pages 237-250.
    8. Marcel Nutz, 2010. "Risk Aversion Asymptotics for Power Utility Maximization," Papers 1003.3582, arXiv.org.
    9. Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
    10. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    11. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    12. Bouchard, Bruno & Pham, Huyen, 2004. "Wealth-Path Dependent Utility Maximization in Incomplete Markets," Economics Papers from University Paris Dauphine 123456789/1803, Paris Dauphine University.
    13. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    14. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
    15. Larsen, Kasper & Zitkovic, Gordan, 2007. "Stability of utility-maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1642-1662, November.
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    Cited by:
    1. Hao Xing, 2012. "Stability of the exponential utility maximization problem with respect to preferences," Papers 1205.6160, arXiv.org, revised Sep 2013.

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