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Continuity Of Utility‐Maximization With Respect To Preferences

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  • Kasper Larsen

Abstract

This paper provides an easily verifiable regularity condition under which the investor's utility maximizer depends continuously on the description of her preferences in a general incomplete financial setting. Specifically, we extend the setting of Jouini and Napp to include noise generated by a general continuous semi‐martingale and to the case where the market price of risk process is allowed to be a general adapted process satisfying a mild integrability condition. This extension allows us to obtain positive results for both the mean‐reversion model of Kim and Omberg and the stochastic volatility model of Heston. Finally, we provide an example set in Samuelson's complete financial model illustrating that without imposing additional regularity, the continuity property of the investor's optimizer can fail.

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  • Kasper Larsen, 2009. "Continuity Of Utility‐Maximization With Respect To Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 237-250, April.
    • Handle: RePEc:bla:mathfi:v:19:y:2009:i:2:p:237-250
    DOI: 10.1111/j.1467-9965.2009.00365.x
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    Cited by:

    1. Pietro Siorpaes, 2015. "Optimal investment and price dependence in a semi-static market," Finance and Stochastics, Springer, vol. 19(1), pages 161-187, January.
    2. Gordan Žitković, 2012. "An example of a stochastic equilibrium with incomplete markets," Finance and Stochastics, Springer, vol. 16(2), pages 177-206, April.
    3. Markus Mocha & Nicholas Westray, 2011. "The Stability of the Constrained Utility Maximization Problem - A BSDE Approach," Papers 1107.0190, arXiv.org.
    4. Astrup Jensen, Bjarne & Marekwica, Marcel, 2011. "Optimal portfolio choice with wash sale constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1916-1937.
    5. Xing, Hao, 2017. "Stability of the exponential utility maximization problem with respect to preferences," LSE Research Online Documents on Economics 57213, London School of Economics and Political Science, LSE Library.
    6. Hao Xing, 2012. "Stability of the exponential utility maximization problem with respect to preferences," Papers 1205.6160, arXiv.org, revised Sep 2013.
    7. Michael Monoyios, 2020. "Infinite horizon utility maximisation from inter-temporal wealth," Papers 2009.00972, arXiv.org, revised Oct 2020.
    8. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
    9. Lingqi Gu & Yiqing Lin & Junjian Yang, 2017. "Utility maximization problem under transaction costs: optimal dual processes and stability," Papers 1710.04363, arXiv.org.
    10. Pietro Siorpaes, 2013. "Optimal investment and price dependence in a semi-static market," Papers 1303.0237, arXiv.org, revised Oct 2013.
    11. Julio Backhoff Veraguas & Francisco Silva, 2015. "Sensitivity analysis for expected utility maximization in incomplete Brownian market models," Papers 1504.02734, arXiv.org, revised Feb 2017.
    12. Kasper Larsen & Halil Mete Soner & Gordan Žitković, 2020. "Conditional Davis pricing," Finance and Stochastics, Springer, vol. 24(3), pages 565-599, July.
    13. Laurence Carassus & Miklós Rásonyi, 2011. "Risk-averse asymptotics for reservation prices," Annals of Finance, Springer, vol. 7(3), pages 375-387, August.
    14. Huy N. Chau & Andrea Cosso & Claudio Fontana & Oleksii Mostovyi, 2015. "Optimal investment with intermediate consumption under no unbounded profit with bounded risk," Papers 1509.01672, arXiv.org, revised Jun 2017.
    15. Michael Monoyios, 2020. "Duality for optimal consumption under no unbounded profit with bounded risk," Papers 2006.04687, arXiv.org, revised Dec 2021.

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