IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2002.00201.html
   My bibliography  Save this paper

Optimal portfolio choice with path dependent labor income: the infinite horizon case

Author

Listed:
  • Enrico Biffis
  • Fausto Gozzi
  • Cecilia Prosdocimi

Abstract

We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and leads to an infinite dimensional stochastic optimal control problem. We solve the problem completely, and find explicitly the optimal controls in feedback form. This is possible because we are able to find an explicit solution to the associated infinite dimensional Hamilton-Jacobi-Bellman (HJB) equation, even if state constraints are present. To the best of our knowledge, this is the first infinite dimensional generalization of Merton's optimal portfolio problem for which explicit solutions can be found. The explicit solution allows us to study the properties of optimal strategies and discuss their financial implications.

Suggested Citation

  • Enrico Biffis & Fausto Gozzi & Cecilia Prosdocimi, 2020. "Optimal portfolio choice with path dependent labor income: the infinite horizon case," Papers 2002.00201, arXiv.org.
    • Handle: RePEc:arx:papers:2002.00201
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2002.00201
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Barucci, Emilio & Gozzi, Fausto & Swiech, Andrzej, 2000. "Incentive compatibility constraints and dynamic programming in continuous time," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 471-508, December.
    2. Costas Meghir & Luigi Pistaferri, 2004. "Income Variance Dynamics and Heterogeneity," Econometrica, Econometric Society, vol. 72(1), pages 1-32, January.
    3. 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.
    4. Hubbard, R Glenn & Skinner, Jonathan & Zeldes, Stephen P, 1995. "Precautionary Saving and Social Insurance," Journal of Political Economy, University of Chicago Press, vol. 103(2), pages 360-399, April.
    5. 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.
    6. 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.
    7. Fatih Guvenen, 2009. "An Empirical Investigation of Labor Income Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(1), pages 58-79, January.
    8. Fatih Guvenen, 2007. "Learning Your Earning: Are Labor Income Shocks Really Very Persistent?," American Economic Review, American Economic Association, vol. 97(3), pages 687-712, June.
    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. Philip H. Dybvig & Hong Liu, 2011. "Verification Theorems for Models of Optimal Consumption and Investment with Retirement and Constrained Borrowing," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 620-635, November.
    11. 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.
    12. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    13. 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.
    14. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(3), pages 427-432, June.
    15. Kjetil Storesletten & Chris I. Telmer & Amir Yaron, 2004. "Cyclical Dynamics in Idiosyncratic Labor Market Risk," Journal of Political Economy, University of Chicago Press, vol. 112(3), pages 695-717, June.
    16. Fabbri Giorgio & Federico Salvatore, 2014. "On the Infinite-Dimensional Representation of Stochastic Controlled Systems with Delayed Control in the Diffusion Term," Mathematical Economics Letters, De Gruyter, vol. 2(3-4), pages 33-43, November.
    17. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    18. Bodie, Zvi & Merton, Robert C. & Samuelson, William F., 1992. "Labor supply flexibility and portfolio choice in a life cycle model," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 427-449.
    19. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(4), pages 629-637, August.
    20. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(5), pages 777-788, October.
    21. Zhu, Yingzi & Zhou, Guofu, 2009. "Technical analysis: An asset allocation perspective on the use of moving averages," Journal of Financial Economics, Elsevier, vol. 92(3), pages 519-544, June.
    22. Markus Reiß, 2002. "Minimax Rates for Nonparametric Drift Estimation in Affine Stochastic Delay Differential Equations," Statistical Inference for Stochastic Processes, Springer, vol. 5(2), pages 131-152, May.
    23. MaCurdy, Thomas E., 1982. "The use of time series processes to model the error structure of earnings in a longitudinal data analysis," Journal of Econometrics, Elsevier, vol. 18(1), pages 83-114, January.
    24. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(1), pages 151-160, February.
    25. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    26. Robert A. Moffitt & Peter Gottschalk, 2002. "Trends in the Transitory Variance of Earnings in the United States," Economic Journal, Royal Economic Society, vol. 112(478), pages 68-73, March.
    27. Abowd, John M & Card, David, 1989. "On the Covariance Structure of Earnings and Hours Changes," Econometrica, Econometric Society, vol. 57(2), pages 411-445, March.
    28. Frédéric Zumer & Jacques Le Cacheux & Marc Flandreau, 1998. "Stability without a pact? Lessons from the European Gold Standard, 1880-1913," Sciences Po publications n°98-01, Sciences Po.
    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. 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, October.
    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. 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.
    4. 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.
    5. 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.
    6. Baltas, I. & Dopierala, L. & Kolodziejczyk, K. & Szczepański, M. & Weber, G.-W. & Yannacopoulos, A.N., 2022. "Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1162-1174.
    7. 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.

    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. Masakatsu Okubo, 2015. "Earnings Dynamics and Profile Heterogeneity: Estimates from Japanese Panel Data," The Japanese Economic Review, Japanese Economic Association, vol. 66(1), pages 112-146, March.
    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, October.
    3. Francisco Gomes & Michael Haliassos & Tarun Ramadorai, 2021. "Household Finance," Journal of Economic Literature, American Economic Association, vol. 59(3), pages 919-1000, September.
    4. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2014. "Consumption and Labor Supply with Partial Insurance: An Analytical Framework," American Economic Review, American Economic Association, vol. 104(7), pages 2075-2126, July.
    5. Tao Wang, 2023. "Perceived versus Calibrated Income Risks in Heterogeneous-Agent Consumption Models," Staff Working Papers 23-59, Bank of Canada.
    6. Whalley, Alexander, 2011. "Education and labor market risk: Understanding the role of data cleaning," Economics of Education Review, Elsevier, vol. 30(3), pages 528-545, June.
    7. 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.
    8. 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.
    9. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2009. "Quantitative Macroeconomics with Heterogeneous Households," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 319-354, May.
    10. Fatih Guvenen, 2009. "An Empirical Investigation of Labor Income Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(1), pages 58-79, January.
    11. Estelle Dauchy & Francisco Navarro-Sanchez & Nathan Seegert, 2021. "Taxation and Inequality: Active and Passive Channels," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 42, pages 156-177, October.
    12. Magnac, Thierry & Pistolesi, Nicolas & Roux, Sébastien, 2013. "Post schooling human capital investments and the life cycle variance of earnings," TSE Working Papers 13-380, Toulouse School of Economics (TSE).
    13. Fatih Guvenen, 2007. "Learning Your Earning: Are Labor Income Shocks Really Very Persistent?," American Economic Review, American Economic Association, vol. 97(3), pages 687-712, June.
    14. Gustavsson, Magnus & Österholm, Pär, 2014. "Does the labor-income process contain a unit root? Evidence from individual-specific time series," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 152-167.
    15. Liu, Xuan & Yang, Fang & Cai, Zongwu, 2016. "Does relative risk aversion vary with wealth? Evidence from households׳ portfolio choice data," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 229-248.
    16. Ivan Vidangos, 2009. "Household welfare, precautionary saving, and social insurance under multiple sources of risk," Finance and Economics Discussion Series 2009-14, Board of Governors of the Federal Reserve System (U.S.).
    17. Hamish Low & Costas Meghir & Luigi Pistaferri, 2010. "Wage Risk and Employment Risk over the Life Cycle," American Economic Review, American Economic Association, vol. 100(4), pages 1432-1467, September.
    18. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.
    19. Manuel Sanchez & Felix Wellschmied, 2020. "Modeling Life-Cycle Earnings Risk with Positive and Negative Shocks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 37, pages 103-126, July.
    20. Fatih Guvenen & Burhanettin Kuruscu, 2010. "A Quantitative Analysis of the Evolution of the US Wage Distribution, 1970–2000," NBER Chapters, in: NBER Macroeconomics Annual 2009, Volume 24, pages 227-276, National Bureau of Economic Research, Inc.

    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:2002.00201. 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.