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

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  • 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.

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    5. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    6. 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.
    7. Jean-Pierre Fouque & Zhaoyu Zhang, 2018. "Mean Field Game with Delay: A Toy Model," Risks, MDPI, vol. 6(3), pages 1-17, September.
    8. 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.
    9. 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.
    10. Enrico Biffis & Fausto Gozzi & Cecilia Prosdocimi, 2020. "Optimal portfolio choice with path dependent labor income: the infinite horizon case," Papers 2002.00201, arXiv.org.
    11. Ji-Won Park & Chae Un Kim, 2020. "Getting to a feasible income equality," Papers 2011.09119, arXiv.org, revised Mar 2021.
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    1. 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, February.
    2. 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.
    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.

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