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Optimal consumption under adjustment costs with respect to multiple reference levels

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Yijie Huang, Kaixin Yan, Qinyi Zhang

Optimization and Control · Submitted 24 Mar 2025

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim By employing the dual transform, the smooth-fit conditions and the super-contact conditions, we obtain the closed-form solution of the dual PDE problem, and can characterize the optimal investment and consumption controls in the piecewise feedback form.

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arXiv ID2503.18443 (version 1)
Pith IDYSHCBA6J, Pith's permanent record of this paper and its review
CitationKaixin Yan, Qinyi Zhang, Yijie Huang. "Optimal consumption under adjustment costs with respect to multiple reference levels." arXiv:2503.18443 (2025). https://pith.science/paper/YSHCBA6J
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,621 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.03 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

This paper studies a type of consumption preference where some adjustment costs are incured whenever the past spending maximum and the past spending minimum records are updated. This preference can capture the adverse effects of the historical consumption high and low values on the agent's consumption performance, thereby matching with some empirically observed smooth consumption patterns. By employing the dual transform, the smooth-fit conditions and the super-contact conditions, we obtain the closed-form solution of the dual PDE problem, and can characterize the optimal investment and consumption controls in the piecewise feedback form. We provide the rigorous proof of the verification theorem and compensate the theoretical findings with some numerical examples and financial implications.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper studies a type of consumption preference where some adjustment costs are incured whenever the past spending maximum and the past spending minimum records are updated. contribution 0.87 0.37 0.04 asserted 0.99
s1 This preference can capture the adverse effects of the historical consumption high and low values on the agent's consumption performance, thereby matching with some empirically observed smooth consumption patterns. interpretation 0.79 0.28 0.11 hedged possibility 0.52
s2 By employing the dual transform, the smooth-fit conditions and the super-contact conditions, we obtain the closed-form solution of the dual PDE problem, and can characterize the optimal investment and consumption controls in the piecewise feedback form. method 0.64 0.96 0.50 asserted 1.00
s3 We provide the rigorous proof of the verification theorem and compensate the theoretical findings with some numerical examples and financial implications. contribution 0.93 0.95 0.12 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This paper studies a type of consumption preference where some adjustment costs are incured whenever the past spending maximum and the past spending minimum records are updated. This preference can capture the adverse effects of the historical consumption high and low values on the agent's consumption performance, thereby matching with some empirically observed smooth consumption patterns. By employing the dual transform, the smooth-fit conditions and the super-contact conditions, we obtain the closed-form solution of the dual PDE problem, and can characterize the optimal investment and consumption controls in the piecewise feedback form. We provide the rigorous proof of the verification theorem and compensate the theoretical findings with some numerical examples and financial implications.

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites

Cites as background 1 paper
  • The multiplicative habit formation has also gained a lot of attention, which generates the utility on the ratio of consumption rate and the habit formation process; see, [ref] , [ref] , [ref] , [ref] , [ref] , to name a few.

    2406.20063 · Introduction · 0.99

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