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Viscosity properties with singularities in a state-constrained expected utility maximization problem

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Mourad Lazgham

Mathematical Finance · Submitted 13 Oct 2015

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

The authors' main claim On the other hand, we establish a comparison principle, which allows us to characterize our value function as the unique viscosity solution of the HJB equation.

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arXiv ID1510.03584 (version 1)
Pith IDLYBHVCP7, Pith's permanent record of this paper and its review
CitationMourad Lazgham. "Viscosity properties with singularities in a state-constrained expected utility maximization problem." arXiv:1510.03584 (2015). https://pith.science/paper/LYBHVCP7
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,044 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.56 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.06 · mentions code or data availability 0.01.

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

We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity. On one hand, we give a so-called verification argument based on the dynamic programming principle, which allows us to derive conditions under which a classical solution of the HJB equation coincides with our value function (provided that it is smooth enough). On the other hand, we establish a comparison principle, which allows us to characterize our value function as the unique viscosity solution of the HJB equation.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity. contribution 0.80 0.89 0.28 asserted 1.00
s1 On one hand, we give a so-called verification argument based on the dynamic programming principle, which allows us to derive conditions under which a classical solution of the HJB equation coincides with our value function (provided that it is smooth enough). method 0.60 0.94 0.11 asserted 0.93
s2 On the other hand, we establish a comparison principle, which allows us to characterize our value function as the unique viscosity solution of the HJB equation. contribution 0.54 0.95 0.47 asserted 1.00

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

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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

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Original abstract

We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity. On one hand, we give a so-called verification argument based on the dynamic programming principle, which allows us to derive conditions under which a classical solution of the HJB equation coincides with our value function (provided that it is smooth enough). On the other hand, we establish a comparison principle, which allows us to characterize our value function as the unique viscosity solution of the HJB equation.

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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

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