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Optimal consumption under loss-averse multiplicative habit-formation preferences

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  • Bahman Angoshtari
  • Xiang Yu
  • Fengyi Yuan

Abstract

This paper studies a loss-averse version of the multiplicative habit formation preference and the corresponding optimal investment and consumption strategies over an infinite horizon. The agent's consumption preference is depicted by a general S-shaped utility function of her consumption-to-habit ratio. By considering the concave envelope of the S-shaped utility and the associated dual value function, we provide a thorough analysis of the HJB equation for the concavified problem via studying a related nonlinear free boundary problem. Based on established properties of the solution to this free boundary problem, we obtain the optimal consumption and investment policies in feedback form. Some new and technical verification arguments are developed to cope with generality of the utility function. The equivalence between the original problem and the concavified problem readily follows from the structure of the feedback policies. We also discuss some quantitative properties of the optimal policies under several commonly used S-shaped utilities, complemented by illustrative numerical examples and their financial implications.

Suggested Citation

  • Bahman Angoshtari & Xiang Yu & Fengyi Yuan, 2024. "Optimal consumption under loss-averse multiplicative habit-formation preferences," Papers 2406.20063, arXiv.org.
    • Handle: RePEc:arx:papers:2406.20063
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    References listed on IDEAS

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    1. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    2. Detemple, Jerome B & Zapatero, Fernando, 1991. "Asset Prices in an Exchange Economy with Habit Formation," Econometrica, Econometric Society, vol. 59(6), pages 1633-1657, November.
    3. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    4. 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.
    5. Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3560-3589, November.
    6. Xiang Yu, 2011. "Utility maximization with addictive consumption habit formation in incomplete semimartingale markets," Papers 1112.2940, arXiv.org, revised May 2015.
    7. 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.
    8. Xue Dong He & Xun Yu Zhou, 2014. "Myopic loss aversion, reference point, and money illusion," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1541-1554, September.
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