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Optimal consumption with loss aversion and reference to past spending maximum

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  • Xun Li
  • Xiang Yu
  • Qinyi Zhang

Abstract

This paper studies an optimal consumption problem for a loss-averse agent with reference to past consumption maximum. To account for loss aversion on relative consumption, an S-shaped utility is adopted that measures the difference between the non-negative consumption rate and a fraction of the historical spending peak. We consider the concave envelope of the utility with respect to consumption, allowing us to focus on an auxiliary HJB variational inequality on the strength of concavification principle and dynamic programming arguments. By applying the dual transform and smooth-fit conditions, the auxiliary HJB variational inequality is solved in piecewise closed-form and some thresholds of the wealth variable are obtained. The optimal consumption and investment control can be derived in the piecewise feedback form. The rigorous verification proofs on optimality and concavification principle are provided. Some numerical sensitivity analysis and financial implications are also presented.

Suggested Citation

  • Xun Li & Xiang Yu & Qinyi Zhang, 2021. "Optimal consumption with loss aversion and reference to past spending maximum," Papers 2108.02648, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2108.02648
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    References listed on IDEAS

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    1. Lijun Bo & Yijie Huang & Kaixin Yan & Xiang Yu, 2024. "Optimal consumption under relaxed benchmark tracking and consumption drawdown constraint," Papers 2410.16611, arXiv.org.
    2. Lijun Bo & Shihua Wang & Xiang Yu, 2022. "A mean field game approach to equilibrium consumption under external habit formation," Papers 2206.13341, arXiv.org, revised Mar 2024.

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