IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v54y2014icp84-96.html
   My bibliography  Save this article

Ratchet consumption over finite and infinite planning horizons

Author

Listed:
  • Watson, John G.
  • Scott, Jason S.

Abstract

Ratchet consumers want their spending to always increase and never decrease. We find an optimal consumption rule for ratchet consumers by maximizing an expected utility that eschews spending declines, yet permits a range of choices for felicity and time preference functions. This solution can be tailored to fit both retirees with finite planning horizons and endowments with infinite planning horizons. We assume complete markets modeled by a pricing kernel generated by a Lévy process. When the kernel is log-normal, we obtain closed-form solutions for both finite and infinite horizons.

Suggested Citation

  • Watson, John G. & Scott, Jason S., 2014. "Ratchet consumption over finite and infinite planning horizons," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 84-96.
    • Handle: RePEc:eee:mateco:v:54:y:2014:i:c:p:84-96
    DOI: 10.1016/j.jmateco.2014.09.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406814001116
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2014.09.001?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. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    2. Mark Schroder & Costis Skiadas, 2002. "An Isomorphism Between Asset Pricing Models With and Without Linear Habit Formation," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1189-1221.
    3. Jason Scott & John Watson, 2013. "The Floor-Leverage Rule for Retirement," Discussion Papers 13-013, Stanford Institute for Economic Policy Research.
    4. Dorje C. Brody & Lane P. Hughston & Ewan Mackie, 2011. "General Theory of Geometric L\'evy Models for Dynamic Asset Pricing," Papers 1111.2169, arXiv.org, revised Jan 2012.
    5. Riedel, Frank, 2009. "Optimal consumption choice with intolerance for declining standard of living," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 449-464, July.
    6. Philip H. Dybvig, 1995. "Dusenberry's Ratcheting of Consumption: Optimal Dynamic Consumption and Investment Given Intolerance for any Decline in Standard of Living," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(2), pages 287-313.
    7. Hindy, Ayman & Huang, Chi-fu & Kreps, David, 1992. "On intertemporal preferences in continuous time : The case of certainty," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 401-440.
    8. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    9. Antonis Papapantoleon, 2008. "An introduction to L\'{e}vy processes with applications in finance," Papers 0804.0482, arXiv.org, revised Nov 2008.
    10. Hindy, Ayman & Huang, Chi-fu, 1993. "Optimal Consumption and Portfolio Rules with Durability and Local Substitution," Econometrica, Econometric Society, vol. 61(1), pages 85-121, January.
    11. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    12. Hindy, Ayman & Huang, Chi-fu, 1992. "Intertemporal Preferences for Uncertain Consumption: A Continuous Time Approach," Econometrica, Econometric Society, vol. 60(4), pages 781-801, July.
    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. Jeon, Junkee & Koo, Hyeng Keun & Shin, Yong Hyun, 2018. "Portfolio selection with consumption ratcheting," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 153-182.
    2. Zhou Yang & Hyeng Keun Koo, 2018. "Optimal Consumption and Portfolio Selection with Early Retirement Option," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1378-1404, November.
    3. Ferrari, Giorgio & Li, Hanwu & Riedel, Frank, 2020. "Optimal Consumption with Intertemporal Substitution under Knightian Uncertainty," Center for Mathematical Economics Working Papers 641, Center for Mathematical Economics, Bielefeld University.
    4. Jeon, Junkee & Park, Kyunghyun, 2020. "Dynamic asset allocation with consumption ratcheting post retirement," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    5. Christopher Biolsi & H. Youn Kim, 2021. "Analyzing state government spending: balanced budget rules or forward-looking decisions?," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 28(4), pages 1035-1079, August.
    6. Jeon, Junkee & Koo, Hyeng Keun & Park, Kyunghyun, 2021. "Finite horizon portfolio selection with durable goods," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 55-67.

    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. Xianzhe Chen & Weidong Tian, 2014. "Optimal portfolio choice and consistent performance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 453-474, October.
    2. Choi, Kyoung Jin & Jeon, Junkee & Koo, Hyeng Keun, 2022. "Intertemporal preference with loss aversion: Consumption and risk-attitude," Journal of Economic Theory, Elsevier, vol. 200(C).
    3. Zvi Bodie & Jérôme Detemple & Marcel Rindisbacher, 2009. "Life-Cycle Finance and the Design of Pension Plans," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 249-286, November.
    4. Ferrari, Giorgio & Li, Hanwu & Riedel, Frank, 2020. "Optimal Consumption with Intertemporal Substitution under Knightian Uncertainty," Center for Mathematical Economics Working Papers 641, Center for Mathematical Economics, Bielefeld University.
    5. Jeon, Junkee & Koo, Hyeng Keun & Park, Kyunghyun, 2021. "Finite horizon portfolio selection with durable goods," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 55-67.
    6. Francisco Gomes & Alexander Michaelides, 2003. "Portfolio Choice With Internal Habit Formation: A Life-Cycle Model With Uninsurable Labor Income Risk," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 729-766, October.
    7. Martins-da-Rocha, V. Filipe & Riedel, Frank, 2010. "On equilibrium prices in continuous time," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1086-1112, May.
    8. Qian Lin & Frank Riedel, 2014. "Optimal consumption and portfolio choice with ambiguity," Papers 1401.1639, arXiv.org.
    9. Zhou, Y., 2014. "Essays on habit formation and inflation hedging," Other publications TiSEM 4886da12-1b84-4fd9-aa07-3, Tilburg University, School of Economics and Management.
    10. Anderson, Robert M. & Raimondo, Roberto C., 2007. "Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets," Department of Economics, Working Paper Series qt0zq6v5gd, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    11. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    12. Drouhin, Nicolas, 2020. "Non-stationary additive utility and time consistency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 1-14.
    13. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    14. Servaas van Bilsen & Roger J. A. Laeven & Theo E. Nijman, 2020. "Consumption and Portfolio Choice Under Loss Aversion and Endogenous Updating of the Reference Level," Management Science, INFORMS, vol. 66(9), pages 3927-3955, September.
    15. Konicz, Agnieszka Karolina & Mulvey, John M., 2015. "Optimal savings management for individuals with defined contribution pension plans," European Journal of Operational Research, Elsevier, vol. 243(1), pages 233-247.
    16. Spaenjers, Christophe & Spira, Sven Michael, 2015. "Subjective life horizon and portfolio choice," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 94-106.
    17. Andréasson, Johan G. & Shevchenko, Pavel V. & Novikov, Alex, 2017. "Optimal consumption, investment and housing with means-tested public pension in retirement," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 32-47.
    18. Hindy, Ayman & Huang, Chi-fu & Zhu, Steven H., 1997. "Optimal consumption and portfolio rules with durability and habit formation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 525-550.
    19. Jeon, Junkee & Park, Kyunghyun, 2020. "Dynamic asset allocation with consumption ratcheting post retirement," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    20. Nicolas Drouhin, 2016. "Non stationary additive utility and time consistency," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01238584, HAL.

    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:mateco:v:54:y:2014:i:c:p:84-96. 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/locate/jmateco .

    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.