IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2002.09445.html
   My bibliography  Save this paper

Stability of the indirect utility process

Author

Listed:
  • Oleksii Mostovyi

Abstract

We investigate the dynamic stability of the indirect utility process associated with a (possibly suboptimal) trading strategy under perturbations of the market. Establishing the reverse conjugacy characterizations first, we prove continuity and first-order convergence of the indirect-utility process under simultaneous perturbations of the finite variation and martingale parts of the return of the risky asset.

Suggested Citation

  • Oleksii Mostovyi, 2020. "Stability of the indirect utility process," Papers 2002.09445, arXiv.org.
    • Handle: RePEc:arx:papers:2002.09445
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2002.09445
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hardy Hulley & Martin Schweizer, 2010. "M6 - On Minimal Market Models and Minimal Martingale Measures," Research Paper Series 280, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Erhan Bayraktar & Ross Kravitz, 2010. "On the Stability of Utility Maximization Problems," Papers 1010.4322, arXiv.org, revised Mar 2011.
    3. Levon Avanesyan & Mykhaylo Shkolnikov & Ronnie Sircar, 2018. "Construction of Forward Performance Processes in Stochastic Factor Models and an Extension of Widder's Theorem," Papers 1805.04535, arXiv.org.
    4. Mostovyi, Oleksii, 2020. "Asymptotic analysis of the expected utility maximization problem with respect to perturbations of the numéraire," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4444-4469.
    5. 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.
    6. Hutton, James E. & Nelson, Paul I., 1984. "Interchanging the order of differentiation and stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 18(2), pages 371-377, November.
    7. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Michail Anthropelos & Gordan Žitković, 2010. "Partial equilibria with convex capital requirements: existence, uniqueness and stability," Annals of Finance, Springer, vol. 6(1), pages 107-135, January.
    9. Oleksii Mostovyi, 2015. "Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption," Finance and Stochastics, Springer, vol. 19(1), pages 135-159, January.
    10. Ioannis Karatzas & Constantinos Kardaras, 2015. "Optional Decomposition for continuous semimartingales under arbitrary filtrations," Papers 1501.04274, arXiv.org, revised Feb 2015.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ashley Davey & Michael Monoyios & Harry Zheng, 2021. "Duality for optimal consumption with randomly terminating income," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1275-1314, October.
    2. Michael Monoyios, 2020. "Infinite horizon utility maximisation from inter-temporal wealth," Papers 2009.00972, arXiv.org, revised Oct 2020.
    3. Oleksii Mostovyi & Mihai Sîrbu, 2019. "Sensitivity analysis of the utility maximisation problem with respect to model perturbations," Finance and Stochastics, Springer, vol. 23(3), pages 595-640, July.
    4. Michael Monoyios, 2020. "Duality for optimal consumption under no unbounded profit with bounded risk," Papers 2006.04687, arXiv.org, revised Dec 2021.
    5. Oleksii Mostovyi & Mihai S^irbu, 2017. "Sensitivity analysis of the utility maximization problem with respect to model perturbations," Papers 1705.08291, arXiv.org.
    6. Michael Monoyios & Oleksii Mostovyi, 2022. "Stability of the Epstein-Zin problem," Papers 2208.09895, arXiv.org, revised Apr 2023.
    7. Berkaoui, Abdelkarem, 2023. "On the optional and orthogonal decompositions of supermartingales and applications," Statistics & Probability Letters, Elsevier, vol. 199(C).
    8. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio without NFLVR: existence, complete characterization, and duality," Papers 1807.06449, arXiv.org.
    9. Kardaras, Constantinos, 2024. "Stochastic integration with respect to arbitrary collections of continuous semimartingales and applications to mathematical finance," LSE Research Online Documents on Economics 121057, London School of Economics and Political Science, LSE Library.
    10. Michail Anthropelos & Tianran Geng & Thaleia Zariphopoulou, 2020. "Competition in Fund Management and Forward Relative Performance Criteria," Papers 2011.00838, arXiv.org.
    11. Huy N. Chau & Andrea Cosso & Claudio Fontana, 2018. "The value of informational arbitrage," Papers 1804.00442, arXiv.org.
    12. Oleksii Mostovyi, 2017. "Optimal consumption of multiple goods in incomplete markets," Papers 1705.02291, arXiv.org, revised Jan 2018.
    13. Ashley Davey & Michael Monoyios & Harry Zheng, 2020. "Duality for optimal consumption with randomly terminating income," Papers 2011.00732, arXiv.org, revised May 2021.
    14. Robert Jarrow & Siguang Li, 2021. "Concavity, stochastic utility, and risk aversion," Finance and Stochastics, Springer, vol. 25(2), pages 311-330, April.
    15. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2021. "Optimal investment, derivative demand, and arbitrage under price impact," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 3-35, January.
    16. Constantinos Kardaras, 2019. "Stochastic integration with respect to arbitrary collections of continuous semimartingales and applications to Mathematical Finance," Papers 1908.03946, arXiv.org, revised Aug 2019.
    17. Westray, Nicholas & Zheng, Harry, 2009. "Constrained nonsmooth utility maximization without quadratic inf convolution," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1561-1579, May.
    18. Christa Cuchiero, 2017. "Polynomial processes in stochastic portfolio theory," Papers 1705.03647, arXiv.org.
    19. Bank, Peter & Riedel, Frank, 1999. "Optimal consumption choice under uncertainty with intertemporal substitution," SFB 373 Discussion Papers 1999,71, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    20. Huy N. Chau & Miklos Rasonyi, 2016. "On optimal investment with processes of long or negative memory," Papers 1608.00768, arXiv.org, revised Mar 2017.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2002.09445. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.