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Forward-backward systems for expected utility maximization

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  • Ulrich Horst
  • Ying Hu
  • Peter Imkeller
  • Anthony Reveillac

Abstract

In this paper we deal with the utility maximization problem with a general utility function. We derive a new approach in which we reduce the utility maximization prob- lem with general utility to the study of a fully-coupled Forward-Backward Stochastic Differential Equation (FBSDE).

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2011-061.pdf
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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2011-061.

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Length: 34 pages
Date of creation: Oct 2011
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2011-061

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Keywords: utility maximization;

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References

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  1. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
  2. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
  3. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility-Based Pricing," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 19(1), pages 129-159.
  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.
  5. Imkeller, Peter & Réveillac, Anthony & Zhang, Jianing, 2011. "Solvability and numerical simulation of BSDEs related to BSPDEs with applications to utility maximization," Economics Papers from University Paris Dauphine 123456789/7101, Paris Dauphine University.
  6. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
  7. Kasper Larsen, 2011. "A note on the existence of the power investor’s optimizer," Finance and Stochastics, Springer, vol. 15(1), pages 183-190, January.
  8. Peter Imkeller & Anthony Réveillac & Jianing Zhang, 2011. "SOLVABILITY AND NUMERICAL SIMULATION OF BSDEs RELATED TO BSPDEs WITH APPLICATIONS TO UTILITY MAXIMIZATION," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 14(05), pages 635-667.
  9. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 99(2), pages 209-286, June.
  10. Ulrich Horst & Traian A. Pirvu & Gonçalo Dos Reis, 2010. "On Securitization, Market Completion and Equilibrium Risk Transfer," SFB 649 Discussion Papers SFB649DP2010-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  11. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293, arXiv.org.
  12. Marcel Nutz, 2009. "The Opportunity Process for Optimal Consumption and Investment with Power Utility," Papers 0912.1879, arXiv.org, revised Jun 2010.
  13. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 10(2), pages 259-276.
  14. Larsen, Kasper & Zitkovic, Gordan, 2007. "Stability of utility-maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 117(11), pages 1642-1662, November.
  15. Freddy Delbaen & Shige Peng & Emanuela Rosazza Gianin, 2010. "Representation of the penalty term of dynamic concave utilities," Finance and Stochastics, Springer, vol. 14(3), pages 449-472, September.
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Citations

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Cited by:
  1. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility," Papers 1202.0608, arXiv.org, revised Sep 2012.
  2. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility," CARF F-Series, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo CARF-F-270, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jun 2012.

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