IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v145y2022icp48-85.html
   My bibliography  Save this article

Optimal portfolio choice with path dependent benchmarked labor income: A mean field model

Author

Listed:
  • Djehiche, Boualem
  • Gozzi, Fausto
  • Zanco, Giovanni
  • Zanella, Margherita

Abstract

We consider the life-cycle optimal portfolio choice problem faced by an agent receiving labor income and allocating her wealth to risky assets and a riskless bond subject to a borrowing constraint. In this paper, to reflect a realistic economic setting, we propose a model where the dynamics of the labor income has two main features. First, labor income adjusts slowly to financial market shocks, a feature already considered in Biffis et al. (2015). Second, the labor income yi of an agent i is benchmarked against the labor incomes of a population yn≔(y1,y2,…,yn) of n agents with comparable tasks and/or ranks. This last feature has not been considered yet in the literature and is faced taking the limit when n→+∞ so that the problem falls into the family of optimal control of infinite-dimensional McKean–Vlasov Dynamics, which is a completely new and challenging research field.

Suggested Citation

  • Djehiche, Boualem & Gozzi, Fausto & Zanco, Giovanni & Zanella, Margherita, 2022. "Optimal portfolio choice with path dependent benchmarked labor income: A mean field model," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 48-85.
    • Handle: RePEc:eee:spapps:v:145:y:2022:i:c:p:48-85
    DOI: 10.1016/j.spa.2021.11.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441492100199X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2021.11.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Luca Benzoni & Pierre Collin‐Dufresne & Robert S. Goldstein, 2007. "Portfolio Choice over the Life‐Cycle when the Stock and Labor Markets Are Cointegrated," Journal of Finance, American Finance Association, vol. 62(5), pages 2123-2167, October.
    2. William T. Dickens & Lorenz Goette & Erica L. Groshen & Steinar Holden & Julian Messina & Mark E. Schweitzer & Jarkko Turunen & Melanie E. Ward, 2007. "How Wages Change: Micro Evidence from the International Wage Flexibility Project," Journal of Economic Perspectives, American Economic Association, vol. 21(2), pages 195-214, Spring.
    3. Jean-Pierre Fouque & Zhaoyu Zhang, 2018. "Mean Field Game with Delay: A Toy Model," Risks, MDPI, vol. 6(3), pages 1-17, September.
    4. Dybvig, Philip H. & Liu, Hong, 2010. "Lifetime consumption and investment: Retirement and constrained borrowing," Journal of Economic Theory, Elsevier, vol. 145(3), pages 885-907, May.
    5. Hervé Le Bihan & Jérémi Montornès & Thomas Heckel, 2012. "Sticky Wages: Evidence from Quarterly Microeconomic Data," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(3), pages 1-32, July.
    6. Ji-Won Park & Chae Un Kim, 2020. "Getting to a feasible income equality," Papers 2011.09119, arXiv.org, revised Mar 2021.
    7. Enrico Biffis & Beniamin Goldys & Cecilia Prosdocimi & Margherita Zanella, 2015. "A pricing formula for delayed claims: Appreciating the past to value the future," Papers 1505.04914, arXiv.org, revised Jul 2022.
    8. Enrico Biffis & Fausto Gozzi & Cecilia Prosdocimi, 2020. "Optimal portfolio choice with path dependent labor income: the infinite horizon case," Papers 2002.00201, arXiv.org.
    9. Giuseppe Freni & Fausto Gozzi & Neri Salvadori, 2006. "Existence of optimal strategies in linear multisector models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 25-48, September.
    10. Ji-Won Park & Chae Un Kim, 2021. "Getting to a feasible income equality," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-16, March.
    11. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alessandro Calvia & Gianluca Cappa & Fausto Gozzi & Enrico Priola, 2023. "HJB Equations and Stochastic Control on Half-Spaces of Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 710-744, August.
    2. Enrico Biffis & Beniamin Goldys & Cecilia Prosdocimi & Margherita Zanella, 2023. "A pricing formula for delayed claims: appreciating the past to value the future," Mathematics and Financial Economics, Springer, volume 17, number 2, June.
    3. Filippo de Feo & Salvatore Federico & Andrzej 'Swik{e}ch, 2023. "Optimal control of stochastic delay differential equations and applications to path-dependent financial and economic models," Papers 2302.08809, arXiv.org.
    4. Amorino, Chiara & Heidari, Akram & Pilipauskaitė, Vytautė & Podolskij, Mark, 2023. "Parameter estimation of discretely observed interacting particle systems," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 350-386.

    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. Enrico Biffis & Fausto Gozzi & Cecilia Prosdocimi, 2020. "Optimal portfolio choice with path dependent labor income: the infinite horizon case," Papers 2002.00201, arXiv.org.
    2. Enrico Biffis & Beniamin Goldys & Cecilia Prosdocimi & Margherita Zanella, 2023. "A pricing formula for delayed claims: appreciating the past to value the future," Mathematics and Financial Economics, Springer, volume 17, number 2, June.
    3. Enrico Biffis & Beniamin Goldys & Cecilia Prosdocimi & Margherita Zanella, 2015. "A pricing formula for delayed claims: Appreciating the past to value the future," Papers 1505.04914, arXiv.org, revised Jul 2022.
    4. Barucci, Emilio & Biffis, Enrico & Marazzina, Daniele, 2023. "Health insurance, portfolio choice, and retirement incentives," European Journal of Operational Research, Elsevier, vol. 307(2), pages 910-921.
    5. Effrosyni Adamopoulou & Ernesto Villanueva, 2020. "Wage determination and the bite of collective contracts in Italy and Spain: evidence from the metal working industry," Working Papers 2036, Banco de España.
    6. Dirk Becherer & Wilfried Kuissi-Kamdem & Olivier Menoukeu-Pamen, 2023. "Optimal consumption with labor income and borrowing constraints for recursive preferences," Working Papers hal-04017143, HAL.
    7. Emi Nakamura & Jón Steinsson, 2013. "Price Rigidity: Microeconomic Evidence and Macroeconomic Implications," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 133-163, May.
    8. Fougère, Denis & Gautier, Erwan & Roux, Sébastien, 2018. "Wage floor rigidity in industry-level agreements: Evidence from France," Labour Economics, Elsevier, vol. 55(C), pages 72-97.
    9. Luca Benzon & Olena Chyruk, 2015. "The Value and Risk of Human Capital," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 179-200, December.
    10. D. Audenaert & J. Bardaji & R. Lardeux & M. Orand & M. Sicsic, 2014. "Wage Resilience in France since the Great Recession," Documents de Travail de l'Insee - INSEE Working Papers g2014-11, Institut National de la Statistique et des Etudes Economiques.
    11. Sanvi Avouyi-Dovi & Denis Fougère & Erwan Gautier, 2013. "Wage Rigidity, Collective Bargaining, and the Minimum Wage: Evidence from French Agreement Data," The Review of Economics and Statistics, MIT Press, vol. 95(4), pages 1337-1351, October.
    12. Weidong Tian & Zimu Zhu, 2020. "A Portfolio Choice Problem Under Risk Capacity Constraint," Papers 2005.13741, arXiv.org, revised Dec 2021.
    13. Anne Kathrin Funk & Daniel Kaufmann, 2022. "Do Sticky Wages Matter? New Evidence from Matched Firm Survey and Register Data," Economica, London School of Economics and Political Science, vol. 89(355), pages 689-712, July.
    14. Daniel Schaefer & Carl Singleton, 2023. "The Extent of Downward Nominal Wage Rigidity: New Evidence from Payroll Data," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 51, pages 60-76, December.
    15. Patrick Lünnemann & Ladislav Wintr, 2009. "Wages are flexible, aren?t they? evidence from monthly micro wage data," BCL working papers 39, Central Bank of Luxembourg.
    16. repec:dau:papers:123456789/11159 is not listed on IDEAS
    17. Alain Bensoussan & Bong-Gyu Jang & Seyoung Park, 2016. "Unemployment Risks and Optimal Retirement in an Incomplete Market," Operations Research, INFORMS, vol. 64(4), pages 1015-1032, August.
    18. Andreas Georgiadis & Alan Manning, 2014. "The Volatility of Earnings: Evidence from High-Frequency Firm-Level Data," CEP Discussion Papers dp1290, Centre for Economic Performance, LSE.
    19. Lieb, L.M., 2009. "Taking real rigidities seriously: implications for optimal policy design in a currency union," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    20. Jósef Sigurdsson & Rannveig Sigurdardottir, 2011. "Evidence of Nominal Wage Rigidity and Wage Setting from Icelandic Microdata," Economics wp55, Department of Economics, Central bank of Iceland.
    21. Joan Daouli & Michael Demoussis & Nicholas Giannakopoulos & Ioannis Laliotis, 2016. "The 2011 Industrial Relations Reform and Nominal Wage Adjustments in Greece," Journal of Labor Research, Springer, vol. 37(4), pages 460-483, December.

    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:eee:spapps:v:145:y:2022:i:c:p:48-85. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.