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Ratchet consumption over finite and infinite planning horizons

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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 & Park, Kyunghyun, 2020. "Dynamic asset allocation with consumption ratcheting post retirement," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    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.

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