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Stability of exponential utility maximization with respect to market perturbations

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  • Erhan Bayraktar
  • Ross Kravitz
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    Abstract

    We investigate the continuity of expected exponential utility maximization with respect to perturbation of the Sharpe ratio of markets. By focusing only on continuity, we impose weaker regularity conditions than those found in the literature. Specifically, we require, in addition to the $V$-compactness hypothesis of Larsen and \v{Z}itkovi\'c (2007) (ArXiv: 0706.0474), a local $bmo$ hypothesis, a condition which is seen to always be trivially satisfied in the setting of Larsen and \v{Z}itkovi\'c (2007). For markets of the form $S = M + \int \lambda d $, these conditions are simultaneously implied by the existence of a uniform bound on the norm of $\lambda \cdot M$ in a suitable $bmo$ space.

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    File URL: http://arxiv.org/pdf/1107.2716
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1107.2716.

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    Date of creation: Jul 2011
    Date of revision: Dec 2012
    Handle: RePEc:arx:papers:1107.2716

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    1. 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.
    2. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
    3. Martin Schweizer & Christophe Stricker & Freddy Delbaen & Pascale Monat & Walter Schachermayer, 1997. "Weighted norm inequalities and hedging in incomplete markets," Finance and Stochastics, Springer, vol. 1(3), pages 181-227.
    4. 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.
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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.

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