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Optimal Job, Consumption, and Portfolio Choice with Multiple Income–Leisure Regimes.

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Τίτλος: Optimal Job, Consumption, and Portfolio Choice with Multiple Income–Leisure Regimes.
Συγγραφείς: Kim, Geonwoo1 (AUTHOR), Jeon, Junkee2 (AUTHOR) junkeejeon@khu.ac.kr
Πηγή: Mathematics (2227-7390). Aug2026, Vol. 14 Issue 16, p2976. 30p.
Θεματικοί όροι: *Labor market, *Earned income, *Portfolio management (Investments), *Consumption (Economics), *Optimal control theory, *Economic models
Περίληψη: We study an infinite-horizon consumption, portfolio, and job-choice problem in which an investor may move costlessly and reversibly among N income–leisure regimes. Job i provides constant labor income Y i and leisure L i , with higher-income jobs offering less leisure. Merely listing N jobs does not imply that all of them are ever selected: an intermediate job can lie below the upper envelope of the relevant dual payoffs and therefore be economically redundant. We formulate a full-activity condition as a strict ordering of adjacent dual intersection points and prove that it is necessary and sufficient for every job to be optimal on a nonempty state interval. When the condition fails, an explicit upper-hull reduction removes the inactive jobs and converts the problem into an equivalent model with a smaller active set. In the complete-market benchmark, the martingale method reduces the mixed control problem to a one-dimensional dual resolvent. The active switching thresholds are explicit, the remaining coefficients follow from a finite transfer recursion, and strong duality yields the optimal consumption, portfolio, wealth, and job policies. Relative to the classical two-job model, the N-job formulation identifies which intermediate occupations survive, how wealth-region widths differ, and when a nominal job menu collapses to fewer effective choices. Numerical exercises report a failure-of-full-activity case, sensitivity analysis, a two-job comparison, and a simulated wealth/job path. The paper is deliberately theoretical and frictionless: it provides a transparent benchmark for richer empirical and structural models rather than statistically testing the wealth–leisure mechanism. [ABSTRACT FROM AUTHOR]
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  Data: Optimal Job, Consumption, and Portfolio Choice with Multiple Income–Leisure Regimes.
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  Data: <searchLink fieldCode="AR" term="%22Kim%2C+Geonwoo%22">Kim, Geonwoo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Jeon%2C+Junkee%22">Jeon, Junkee</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> junkeejeon@khu.ac.kr</i>
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  Data: <searchLink fieldCode="JN" term="%22Mathematics+%282227-7390%29%22">Mathematics (2227-7390)</searchLink>. Aug2026, Vol. 14 Issue 16, p2976. 30p.
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  Data: *<searchLink fieldCode="DE" term="%22Labor+market%22">Labor market</searchLink><br />*<searchLink fieldCode="DE" term="%22Earned+income%22">Earned income</searchLink><br />*<searchLink fieldCode="DE" term="%22Portfolio+management+%28Investments%29%22">Portfolio management (Investments)</searchLink><br />*<searchLink fieldCode="DE" term="%22Consumption+%28Economics%29%22">Consumption (Economics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Optimal+control+theory%22">Optimal control theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Economic+models%22">Economic models</searchLink>
– Name: Abstract
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  Data: We study an infinite-horizon consumption, portfolio, and job-choice problem in which an investor may move costlessly and reversibly among N income–leisure regimes. Job i provides constant labor income Y i and leisure L i , with higher-income jobs offering less leisure. Merely listing N jobs does not imply that all of them are ever selected: an intermediate job can lie below the upper envelope of the relevant dual payoffs and therefore be economically redundant. We formulate a full-activity condition as a strict ordering of adjacent dual intersection points and prove that it is necessary and sufficient for every job to be optimal on a nonempty state interval. When the condition fails, an explicit upper-hull reduction removes the inactive jobs and converts the problem into an equivalent model with a smaller active set. In the complete-market benchmark, the martingale method reduces the mixed control problem to a one-dimensional dual resolvent. The active switching thresholds are explicit, the remaining coefficients follow from a finite transfer recursion, and strong duality yields the optimal consumption, portfolio, wealth, and job policies. Relative to the classical two-job model, the N-job formulation identifies which intermediate occupations survive, how wealth-region widths differ, and when a nominal job menu collapses to fewer effective choices. Numerical exercises report a failure-of-full-activity case, sensitivity analysis, a two-job comparison, and a simulated wealth/job path. The paper is deliberately theoretical and frictionless: it provides a transparent benchmark for richer empirical and structural models rather than statistically testing the wealth–leisure mechanism. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.3390/math14162976
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 30
        StartPage: 2976
    Subjects:
      – SubjectFull: Labor market
        Type: general
      – SubjectFull: Earned income
        Type: general
      – SubjectFull: Portfolio management (Investments)
        Type: general
      – SubjectFull: Consumption (Economics)
        Type: general
      – SubjectFull: Optimal control theory
        Type: general
      – SubjectFull: Economic models
        Type: general
    Titles:
      – TitleFull: Optimal Job, Consumption, and Portfolio Choice with Multiple Income–Leisure Regimes.
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          Name:
            NameFull: Kim, Geonwoo
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            NameFull: Jeon, Junkee
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          Dates:
            – D: 15
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
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              Value: 14
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              Value: 16
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            – TitleFull: Mathematics (2227-7390)
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