IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2003.01783.html
   My bibliography  Save this paper

Mortality and Healthcare: a Stochastic Control Analysis under Epstein-Zin Preferences

Author

Listed:
  • Joshua Aurand
  • Yu-Jui Huang

Abstract

This paper studies optimal consumption, investment, and healthcare spending under Epstein-Zin preferences. Given consumption and healthcare spending plans, Epstein-Zin utilities are defined over an agent's random lifetime, partially controllable by the agent as healthcare reduces mortality growth. To the best of our knowledge, this is the first time Epstein-Zin utilities are formulated on a controllable random horizon, via an infinite-horizon backward stochastic differential equation with superlinear growth. A new comparison result is established for the uniqueness of associated utility value processes. In a Black-Scholes market, the stochastic control problem is solved through the related Hamilton-Jacobi-Bellman (HJB) equation. The verification argument features a delicate containment of the growth of the controlled morality process, which is unique to our framework, relying on a combination of probabilistic arguments and analysis of the HJB equation. In contrast to prior work under time-separable utilities, Epstein-Zin preferences facilitate calibration. The model-generated mortality closely approximates actual mortality data in the US and UK; moreover, the efficacy of healthcare can be calibrated and compared between the two countries.

Suggested Citation

  • Joshua Aurand & Yu-Jui Huang, 2020. "Mortality and Healthcare: a Stochastic Control Analysis under Epstein-Zin Preferences," Papers 2003.01783, arXiv.org, revised Jul 2021.
  • Handle: RePEc:arx:papers:2003.01783
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2003.01783
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yogo, Motohiro, 2016. "Portfolio choice in retirement: Health risk and the demand for annuities, housing, and risky assets," Journal of Monetary Economics, Elsevier, vol. 80(C), pages 17-34.
    2. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    3. Rosen, Sherwin, 1988. "The Value of Changes in Life Expectancy," Journal of Risk and Uncertainty, Springer, vol. 1(3), pages 285-304, September.
    4. Robert E. Hall & Charles I. Jones, 2007. "The Value of Life and the Rise in Health Spending," The Quarterly Journal of Economics, Oxford University Press, vol. 122(1), pages 39-72.
    5. Costis Skiadas, 1998. "Recursive utility and preferences for information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 293-312.
    6. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    7. Beeler, Jason & Campbell, John Y., 2012. "The Long-Run Risks Model and Aggregate Asset Prices: An Empirical Assessment," Critical Finance Review, now publishers, vol. 1(1), pages 141-182, January.
    8. Grossman, Michael, 1972. "On the Concept of Health Capital and the Demand for Health," Journal of Political Economy, University of Chicago Press, vol. 80(2), pages 223-255, March-Apr.
    9. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," Review of Economic Studies, Oxford University Press, vol. 32(2), pages 137-150.
    10. Harjoat S. Bhamra & Lars-Alexander Kuehn & Ilya A. Strebulaev, 2010. "The Levered Equity Risk Premium and Credit Spreads: A Unified Framework," Review of Financial Studies, Society for Financial Studies, vol. 23(2), pages 645-703, February.
    11. Holger Kraft & Thomas Seiferling & Frank Thomas Seifried, 2017. "Optimal consumption and investment with Epstein–Zin recursive utility," Finance and Stochastics, Springer, vol. 21(1), pages 187-226, January.
    12. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    13. Holger Kraft & Frank Seifried & Mogens Steffensen, 2013. "Consumption-portfolio optimization with recursive utility in incomplete markets," Finance and Stochastics, Springer, vol. 17(1), pages 161-196, January.
    14. Ravi Bansal, 2007. "Long-run risks and financial markets," Review, Federal Reserve Bank of St. Louis, vol. 89(Jul), pages 283-300.
    15. Benzoni, Luca & Collin-Dufresne, Pierre & Goldstein, Robert S., 2011. "Explaining asset pricing puzzles associated with the 1987 market crash," Journal of Financial Economics, Elsevier, vol. 101(3), pages 552-573, September.
    16. Julien Hugonnier & Florian Pelgrin, 2013. "Health and (Other) Asset Holdings," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 663-710.
    17. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    18. Ehrlich, Isaac & Chuma, Hiroyuki, 1990. "A Model of the Demand for Longevity and the Value of Life Extension," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 761-782, August.
    19. Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, vol. 89(1), pages 68-126, November.
    20. Hansen, Lars Peter & Heaton, John & Lee, Junghoon & Roussanov, Nikolai, 2007. "Intertemporal Substitution and Risk Aversion," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 61, Elsevier.
    21. Paolo Guasoni & Yu-Jui Huang, 2019. "Consumption, Investment, and Healthcare with Aging," Papers 1901.00424, arXiv.org, revised Jan 2019.
    22. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
    23. Paolo Guasoni & Yu-Jui Huang, 2019. "Consumption, investment and healthcare with aging," Finance and Stochastics, Springer, vol. 23(2), pages 313-358, April.
    24. Hao Xing, 2017. "Consumption–investment optimization with Epstein–Zin utility in incomplete markets," Finance and Stochastics, Springer, vol. 21(1), pages 227-262, January.
    25. Annette Vissing-Jørgensen & Orazio P. Attanasio, 2003. "Stock-Market Participation, Intertemporal Substitution, and Risk-Aversion," American Economic Review, American Economic Association, vol. 93(2), pages 383-391, May.
    26. Ehrlich, Isaac, 2000. "Uncertain lifetime, life protection, and the value of life saving," Journal of Health Economics, Elsevier, vol. 19(3), pages 341-367, May.
    27. Donald S. Shepard & Richard J. Zeckhauser, 1984. "Survival versus Consumption," Management Science, INFORMS, vol. 30(4), pages 423-439, April.
    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. Giorgio Ferrari & Shihao Zhu, 2022. "Consumption Decision, Portfolio Choice and Healthcare Irreversible Investment," Papers 2212.05317, arXiv.org.
    2. Michael Monoyios & Oleksii Mostovyi, 2022. "Stability of the Epstein-Zin problem," Papers 2208.09895, arXiv.org.
    3. Ferrari, Giorgio & Zhu, Shihao, 2022. "Consumption Descision, Portfolio Choice and Healthcare Irreversible Investment," Center for Mathematical Economics Working Papers 671, Center for Mathematical Economics, Bielefeld University.

    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. Joshua Aurand & Yu-Jui Huang, 2019. "Epstein-Zin Utility Maximization on a Random Horizon," Papers 1903.08782, arXiv.org, revised Dec 2022.
    2. Julien Hugonnier & Florian Pelgrin, 2013. "Health and (Other) Asset Holdings," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 663-710.
    3. Paolo Guasoni & Yu-Jui Huang, 2019. "Consumption, investment and healthcare with aging," Finance and Stochastics, Springer, vol. 23(2), pages 313-358, April.
    4. Zixin Feng & Dejian Tian, 2021. "Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints," Papers 2111.09032, arXiv.org, revised Oct 2022.
    5. Hao Xing, 2015. "Consumption investment optimization with Epstein-Zin utility in incomplete markets," Papers 1501.04747, arXiv.org, revised Nov 2015.
    6. Hao Xing, 2017. "Consumption–investment optimization with Epstein–Zin utility in incomplete markets," Finance and Stochastics, Springer, vol. 21(1), pages 227-262, January.
    7. Chen, Xingjiang & Ruan, Xinfeng & Zhang, Wenjun, 2021. "Dynamic portfolio choice and information trading with recursive utility," Economic Modelling, Elsevier, vol. 98(C), pages 154-167.
    8. Pelgrin, Florian & St-Amour, Pascal, 2016. "Life cycle responses to health insurance status," Journal of Health Economics, Elsevier, vol. 49(C), pages 76-96.
    9. Anis Matoussi & Hao Xing, 2016. "Convex duality for stochastic differential utility," Papers 1601.03562, arXiv.org.
    10. Julien Hugonnier & Florian Pelgrin & Pascal St-Amour, 2010. "A structural analysis of the health expenditures and portfolio choices of retired agents," Swiss Finance Institute Research Paper Series 10-29, Swiss Finance Institute.
    11. Matoussi, Anis & Xing, Hao, 2018. "Convex duality for Epstein-Zin stochastic differential utility," LSE Research Online Documents on Economics 82519, London School of Economics and Political Science, LSE Library.
    12. Kuhn, Michael & Wrzaczek, Stefan & Prskawetz, Alexia & Feichtinger, Gustav, 2015. "Optimal choice of health and retirement in a life-cycle model," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 186-212.
    13. Shigeta, Yuki, 2020. "Gain/loss asymmetric stochastic differential utility," Journal of Economic Dynamics and Control, Elsevier, vol. 118(C).
    14. Holger Kraft & Frank Seifried & Mogens Steffensen, 2013. "Consumption-portfolio optimization with recursive utility in incomplete markets," Finance and Stochastics, Springer, vol. 17(1), pages 161-196, January.
    15. Shigeta, Yuki, 2022. "Quasi-hyperbolic discounting under recursive utility and consumption–investment decisions," Journal of Economic Theory, Elsevier, vol. 204(C).
    16. Ryan Edwards, 2013. "The cost of uncertain life span," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(4), pages 1485-1522, October.
    17. Kuhn, Michael & Frankovic, Ivan & Wrzaczek, Stefan, 2017. "Medical Progress, Demand for Health Care, and Economic Performance," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168249, Verein für Socialpolitik / German Economic Association.
    18. Julien Hugonnier & Florian Pelgrin & Pascal St‐Amour, 2020. "Closing down the shop: Optimal health and wealth dynamics near the end of life," Health Economics, John Wiley & Sons, Ltd., vol. 29(2), pages 138-153, February.
    19. Antoine Bommier & Daniel Harenberg & François Le Grand & Cormac O'Dea, 2020. "Recursive Preferences, the Value of Life, and Household Finance," Cowles Foundation Discussion Papers 2231, Cowles Foundation for Research in Economics, Yale University.
    20. Kuhn, Michael & Wrzaczek, Stefan & Prskawetz, Alexia & Feichtinger, Gustav, 2011. "Externalities in a life cycle model with endogenous survival," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 627-641.

    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:2003.01783. See general information about how to correct material in RePEc.

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

    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 hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.