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2006 Fiscal Year Final Research Report Summary

Viscosity solutions of nonlinear variational inequalities and their applications

Research Project

Project/Area Number 16540160
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionEhime University

Principal Investigator

MORIMOTO Hiroaki  EhimeUniversity, Graduate School of Science and Engineering, Professor, 理工学研究科, 教授 (80166438)

Co-Investigator(Kenkyū-buntansha) KAWAGUCHI Kazuhito  Ehime University, Faculty of Law and Letters, Associate Professor, 法文学部, 助教授 (30234040)
ISHIKAWA Yasushi  Ehime University, Graduate School of Science and Engineering, Associate Professor, 理工学研究科, 助教授 (70202976)
Project Period (FY) 2004 – 2006
Keywordsvariational inequalities / viscosity solutions / Dynamic programming / nonlinear elliptic equations
Research Abstract

The purpose of this study is to solve the optimization problems in mathematical economics and mathematical finance by applications of the modern theory in stochastic control. The study in this period focuses on the smoothness of viscosity solutions of the nonlinear variational inequalities and elliptic equations.
Due to the grant, the results will be published in the book entitled:
Stochastic Control and Mathematical Modelling in Economics.
The main idea to solve these optimization problems is summarized as follows:
(a) We formulate the problem and define the value function.
(b) We verify that the Dynamic Programming Principle (DPP) holds for the value function.
(c) By the DPP, the value function becomes a unique viscosity solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with the problem.
(d) By the uniqueness of viscosity solutions and the existence of a unique classical solution of the boundary value problem for the HJB equation, we obtain the smoothness of the viscosity solution of the HJB equation.
(e) By the solution of the HJB equation, we construct an optimal policy.

  • Research Products

    (7 results)

All 2007 2006 2005

All Journal Article (7 results)

  • [Journal Article] Long-run average welfare in a pollution accumulation model2007

    • Author(s)
      K.Kawaguchi, H.Morimoto
    • Journal Title

      Journal of Economic Dynamics and Control 31

      Pages: 703-720

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Long-run average welfare in a pollution accumulation model2007

    • Author(s)
      K.Kawaguchi, H.Morimoto
    • Journal Title

      Journal of Economic Dynamic and Control 31

      Pages: 703-720

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The probabilistic solution of the Dirichlet problem for degenerate elliptic equations2006

    • Author(s)
      C.Liu, H.Morimoto
    • Journal Title

      Bull. Pol. Acad. Sci. Math. 54・2

      Pages: 163-174

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The probabilistic solution of the Dirichlet problem for degenerate elliptic equations2006

    • Author(s)
      C.Liu, H.Morimoto
    • Journal Title

      Bull.Pol.Acad.Sci.Math. 54

      Pages: 163-174

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] An extension of the linear regulator for degenerate diffusions2005

    • Author(s)
      Md.A.Baten, H.Morimoto
    • Journal Title

      IEEE Transactions on Automatic Control 50

      Pages: 1822-1826

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Optimal consumption and portfolio choice with stopping2005

    • Author(s)
      S.Koike, H.Morimoto
    • Journal Title

      Funkcial. Ekvac. 48・2

      Pages: 183-202

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Optimal consumption and portfolio choice with stopping2005

    • Author(s)
      S.Koike, H.Morimoto
    • Journal Title

      Funkcial.Ekvac. 48

      Pages: 183-202

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2008-05-27  

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