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On the dual problem of utility maximization in incomplete markets

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  • Gu, Lingqi
  • Lin, Yiqing
  • Yang, Junjian

Abstract

In this paper, we study the dual problem of the expected utility maximization in incomplete markets with bounded random endowment. We start with the problem formulated in Cvitanić et al. (2001) and prove the following statement: in the Brownian framework, the countably additive part Q̂r of the dual optimizer Q̂∈(L∞)∗ obtained in Cvitanić et al. (2001) can be represented by the terminal value of a supermartingale deflator Y defined in Kramkov and Schachermayer (1999), which is a local martingale.

Suggested Citation

  • Gu, Lingqi & Lin, Yiqing & Yang, Junjian, 2016. "On the dual problem of utility maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1019-1035.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:4:p:1019-1035
    DOI: 10.1016/j.spa.2015.10.009
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    References listed on IDEAS

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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.
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    7. Christoph Czichowsky & Walter Schachermayer & Junjian Yang, 2014. "Shadow prices for continuous processes," Papers 1408.6065, arXiv.org, revised May 2015.
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    10. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility‐Based Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 129-159, January.
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    Cited by:

    1. Kasper Larsen & Halil Mete Soner & Gordan v{Z}itkovi'c, 2017. "Conditional Davis Pricing," Papers 1702.02087, arXiv.org, revised Aug 2018.
    2. Lingqi Gu & Yiqing Lin & Junjian Yang, 2017. "Utility maximization problem under transaction costs: optimal dual processes and stability," Papers 1710.04363, arXiv.org.
    3. Yiqing Lin & Junjian Yang, 2016. "Utility maximization problem with random endowment and transaction costs: when wealth may become negative," Papers 1604.08224, arXiv.org, revised Sep 2016.
    4. Kasper Larsen & Halil Mete Soner & Gordan Žitković, 2020. "Conditional Davis pricing," Finance and Stochastics, Springer, vol. 24(3), pages 565-599, July.
    5. Zixin Feng & Dejian Tian & Harry Zheng, 2024. "Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets," Papers 2407.19995, arXiv.org.

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