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Optimal consumption choice with intolerance for declining standard of living

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  • Riedel, Frank

Abstract

We reconsider the optimal consumption choice of investors who do not tolerate any decline in their consumption rate. We connect the demand behavior of such agents to the behavior of standard time-additive agents. With consumption ratcheting, the investor demands the running maximum of the optimal plan a conventional time-additive investor with lower initial wealth would choose. The analysis is carried out for Lévy processes, in particular for jump-diffusions. We obtain explicit solutions for all Bernoulli utility functions, not only those of CRRA type.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:mateco:v:45:y:2009:i:7-8:p:449-464
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    1. Frank Riedel & Peter Bank, 2001. "Existence and structure of stochastic equilibria with intertemporal substitution," Finance and Stochastics, Springer, vol. 5(4), pages 487-509.
    2. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
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    6. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    7. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    8. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    9. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    10. Ralf Korn, 1997. "Optimal Portfolios:Stochastic Models for Optimal Investment and Risk Management in Continuous Time," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3548, January.
    11. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
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    Cited by:

    1. 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.
    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. Koo, Byung Lim & Koo, Hyeng Keun & Koo, Jung Lim & Hyun, ChongSeok, 2012. "A generalization of Dybvig’s result on portfolio selection with intolerance for decline in consumption," Economics Letters, Elsevier, vol. 117(3), pages 646-649.
    4. 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).
    5. 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.
    6. 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.
    7. Jeon, Junkee & Park, Kyunghyun, 2020. "Dynamic asset allocation with consumption ratcheting post retirement," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    8. Junkee Jeon & Kyunghyun Park, 2021. "Portfolio selection with drawdown constraint on consumption: a generalization model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 243-289, April.

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    More about this item

    Keywords

    Intertemporal consumption choice; Habit formation; Nontime separable utility;
    All these keywords.

    JEL classification:

    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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