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Stability of exponential utility maximization with respect to market perturbations

Author Info

• Erhan Bayraktar
• Ross Kravitz

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

Bibliographic Info

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

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 Length: Date of creation: Jul 2011 Date of revision: Dec 2012 Handle: RePEc:arx:papers:1107.2716 Contact details of provider: Web page: http://arxiv.org/

References

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1. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
2. Marcel Nutz, 2009. "The Opportunity Process for Optimal Consumption and Investment with Power Utility," Papers 0912.1879, arXiv.org, revised Jun 2010.
3. Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 99-123.
4. Gordan Žitković, 2012. "An example of a stochastic equilibrium with incomplete markets," Finance and Stochastics, Springer, vol. 16(2), pages 177-206, April.
5. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
6. 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.
7. 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.
8. 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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