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Equilibrium controls in time inconsistent stochastic linear quadratic problems

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Tianxiao Wang

Optimization and Control · Submitted 4 Feb 2018

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

The authors' main claim Three notions, i.e., closed-loop equilibrium controls/strategies, open-loop equilibrium controls and their closed-loop representations, are characterized in unified manners.

how it is stated · asserted 1.00 read the record →

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arXiv ID1802.01077 (version 1)
Pith IDWQIFBWCF, Pith's permanent record of this paper and its review
CitationTianxiao Wang. "Equilibrium controls in time inconsistent stochastic linear quadratic problems." arXiv:1802.01077 (2018). https://pith.science/paper/WQIFBWCF
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The compiled record

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, 3,581 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.23 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

This paper deals with a class of time inconsistent stochastic linear quadratic (SLQ) optimal control problems in Markovian framework. Three notions, i.e., closed-loop equilibrium controls/strategies, open-loop equilibrium controls and their closed-loop representations, are characterized in unified manners. These results indicate clearer and deeper distinctions among these notions. For example, in particular time consistent setting, the open-loop equilibrium controls are fully characterized by first-order, second-order necessary optimality conditions, and become needlessly optimal, while the closed-loop equilibrium controls naturally reduce into closed-loop optimal controls.

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 deals with a class of time inconsistent stochastic linear quadratic (SLQ) optimal control problems in Markovian framework. background 0.79 0.47 0.04 asserted 0.95
s1 Three notions, i.e., closed-loop equilibrium controls/strategies, open-loop equilibrium controls and their closed-loop representations, are characterized in unified manners. contribution 0.69 0.90 0.31 asserted 1.00
s2 These results indicate clearer and deeper distinctions among these notions. interpretation 0.98 0.82 0.22 hedged possibility 0.83
s3 For example, in particular time consistent setting, the open-loop equilibrium controls are fully characterized by first-order, second-order necessary optimality conditions, and become needlessly optimal, while the closed-loop equilibrium controls naturally reduce into closed-loop optimal controls. result 0.61 0.81 0.25 asserted 0.92

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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  • references and citing sentences
  • relations to other papers
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  • 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 deals with a class of time inconsistent stochastic linear quadratic (SLQ) optimal control problems in Markovian framework. Three notions, i.e., closed-loop equilibrium controls/strategies, open-loop equilibrium controls and their closed-loop representations, are characterized in unified manners. These results indicate clearer and deeper distinctions among these notions. For example, in particular time consistent setting, the open-loop equilibrium controls are fully characterized by first-order, second-order necessary optimality conditions, and become needlessly optimal, while the closed-loop equilibrium controls naturally reduce into closed-loop optimal controls.

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