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On Applications for partial differential equations in non-smooth systems to consumer theory and econometric theory

Research Project

Project/Area Number 21K01403
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 07010:Economic theory-related
Research InstitutionChuo University

Principal Investigator

Hosoya Yuhki  中央大学, 経済学部, 教授 (30383954)

Project Period (FY) 2021-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2023: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2022: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2021: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords積分可能性理論 / 消費者理論 / 均衡理論 / 意思決定理論 / 微分方程式 / 一般均衡理論 / 積分可能性 / 隻分可能性理論 / マクロ動学理論 / 変分法
Outline of Research at the Start

消費者の購買行動から好みを逆算するための数学的理論を経済学の応用研究に使える形にまで整備するのが本研究の目的である。好みの調査は応用研究にとって必要不可欠であるが、一方で単純なアンケート調査などには様々な問題があることがわかってきており、そのためにこの種の理論が必要になる。この理論は消費者理論の内部では積分可能性理論と呼ばれ、微分方程式の深い解析を通じて様々なことが可能になるということがわかってきている。本研究はこの理論の応用可能性をさらに推進するためのものである。

Outline of Final Research Achievements

As of 2024, the paper ``Non-Smooth Integrability Theory'' is published in Economic Theory. This paper is currently only available in electronic form, and will not be officially published in paper until a little later, but it is a confirmed result of this research. This paper can be regarded as the culmination of this research, and the principal investigator believes that this research project has been successfully completed with the publication of this paper.

Academic Significance and Societal Importance of the Research Achievements

一般的に消費者の好みは、対応するデータがないため、推定が困難であることが知られている。本研究課題の成果によって、この消費者の好みの理論的対応物である効用関数を、購買行動の理論的対応物である需要関数から逆算することが可能になった。これはつまり、購買行動を用いて、適切に消費者の好みを推定することが可能になったということを意味する。

Report

(4 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • Research Products

    (21 results)

All 2024 2023 2022 2021

All Journal Article (10 results) (of which Peer Reviewed: 10 results,  Open Access: 10 results) Presentation (11 results) (of which Int'l Joint Research: 3 results)

  • [Journal Article] Non-smooth integrability theory2024

    • Author(s)
      Hosoya Yuhki
    • Journal Title

      Economic Theory

      Volume: 未定 Issue: 2 Pages: 475-520

    • DOI

      10.1007/s00199-024-01564-x

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the fragility of the basis on the Hamilton?Jacobi?Bellman equation in economic dynamics2024

    • Author(s)
      Hosoya Yuhki
    • Journal Title

      Journal of Mathematical Economics

      Volume: 111 Pages: 102940-102940

    • DOI

      10.1016/j.jmateco.2024.102940

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A Rigorous Proof of the Index Theorem for Economists2023

    • Author(s)
      Yuhki Hosoya
    • Journal Title

      Communications in Economics and Mathematical Sciences

      Volume: 2 Issue: 0 Pages: 11-30

    • DOI

      10.50906/cems.2.0_11

    • ISSN
      2436-3162
    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the basis of the Hamilton?Jacobi?Bellman equation in economic dynamics2023

    • Author(s)
      Hosoya Yuhki
    • Journal Title

      Physica D: Nonlinear Phenomena

      Volume: 446 Pages: 133684-133684

    • DOI

      10.1016/j.physd.2023.133684

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Differential characterization of quasi-concave functions without twice differentiability2022

    • Author(s)
      Yuhki Hosoya
    • Journal Title

      Communications in Optimization Theory

      Volume: 2022 Pages: 2022-21

    • DOI

      10.23952/cot.2022.21

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] An axiom for concavifiable preferences in view of Alt’s theory2022

    • Author(s)
      Hosoya Yuhki
    • Journal Title

      Journal of Mathematical Economics

      Volume: 98 Pages: 102583-102583

    • DOI

      10.1016/j.jmateco.2021.102583

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the approximate purification of mixed strategies in games with infinite action sets2022

    • Author(s)
      Hosoya Yuhki、Yu Chaowen
    • Journal Title

      Economic Theory Bulletin

      Volume: 10 Issue: 1 Pages: 69-93

    • DOI

      10.1007/s40505-022-00219-1

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Consumer Optimization and a First-Order PDE with a Non-Smooth System2021

    • Author(s)
      Hosoya Yuhki
    • Journal Title

      Operations Research Forum

      Volume: 2 Issue: 4

    • DOI

      10.1007/s43069-021-00104-w

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Continuous adjustments and Smale’s non-tatonnement processes2021

    • Author(s)
      Yu Chaowen、Hosoya Yuhki
    • Journal Title

      Journal of Mathematical Economics

      Volume: 99 Pages: 102619-102619

    • DOI

      10.1016/j.jmateco.2021.102619

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Equivalence between Nikliborc's theorem and Frobenius' theorem2021

    • Author(s)
      Hosoya Yuhki
    • Journal Title

      Pure and Applied Functional Analysis

      Volume: 6 Pages: 719-741

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] Non-Smooth Integrability Theory2023

    • Author(s)
      細矢祐誉
    • Organizer
      2023年度数理経済学会研究集会「数理経済学とその周辺」
    • Related Report
      2023 Annual Research Report
  • [Presentation] Utilitarian Theorems and Equivalence of Utility Theories2023

    • Author(s)
      細矢祐誉
    • Organizer
      日本経済学会2023年度秋期大会
    • Related Report
      2023 Annual Research Report
  • [Presentation] Utilitarian Theorems and Equivalence of Utility Theories2023

    • Author(s)
      細矢祐誉
    • Organizer
      第29回DCコンファレンス
    • Related Report
      2023 Annual Research Report
  • [Presentation] Non-Smooth Integrability Theory2023

    • Author(s)
      Yuhki Hosoya
    • Organizer
      ICIAM2023
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Non-Smooth Frobenius' Theorem2023

    • Author(s)
      Yuhki Hosoya
    • Organizer
      The 13th AIMS conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Violation of the Hamilton-Jacobi-Bellman Equation in Economic Dynamics2022

    • Author(s)
      Yuhki Hosoya
    • Organizer
      ORCOS: VC2022
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the Uniqueness and Stability of the Equilibrium Price in Quasi-Linear Economies2022

    • Author(s)
      細矢祐誉
    • Organizer
      第28回DCコンファレンス
    • Related Report
      2022 Research-status Report
  • [Presentation] Non-Smooth Integrability Theory2022

    • Author(s)
      細矢祐誉
    • Organizer
      日本経済学会2022年度秋期大会
    • Related Report
      2022 Research-status Report
  • [Presentation] On the Uniqueness and Stability of the Equilibrium Price in Quasi-Linear Economies2022

    • Author(s)
      細矢祐誉
    • Organizer
      数理経済学会2022年度研究集会「数理経済学とその周辺」
    • Related Report
      2022 Research-status Report
  • [Presentation] On the Uniqueness and Stability of the Equilibrium Price in Quasi-Linear Economies2021

    • Author(s)
      細矢祐誉
    • Organizer
      日本経済学会2021年度秋期大会
    • Related Report
      2021 Research-status Report
  • [Presentation] The Axiom for Concavifiable Preference in View of Alt's Theory2021

    • Author(s)
      細矢祐誉
    • Organizer
      数理経済学会研究集会「数理経済学とその周辺」
    • Related Report
      2021 Research-status Report

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Published: 2021-04-28   Modified: 2025-01-30  

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