• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2011 Fiscal Year Final Research Report

Theory of viscosity solutions for nonlinear variational inequalities and its applications

Research Project

  • PDF
Project/Area Number 21540188
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  愛媛大学, 大学院・理工学研究科, 教授 (40085494)

Co-Investigator(Kenkyū-buntansha) KAWAGUCHI Kazuhito  愛媛大学, 法文学部, 准教授 (30234040)
ISHIKAWA Yasushi  愛媛大学, 大学院・理工学研究科, 准教授 (70202976)
Project Period (FY) 2009 – 2011
Keywords変分不等式 / 粘性解 / penalty法 / 幾何ブラウン運動 / 確率制御
Research Abstract

The study explored the optimization problem to maximize the utility function for the state described by the stochastic differential equations and the problem of nonlinear variational inequalities on mathematical economics. The research results can be summarized as follows:
(1) Publication of a book
This book provides the mathematical foundation for broader applications to mathematical economics.
(2) Development of the penalty method
The penalty equations are developed to solve nonlinear variational inequalities with gradient constraint.

  • Research Products

    (12 results)

All 2012 2011 2010 2009 Other

All Journal Article (5 results) Presentation (6 results) Book (1 results)

  • [Journal Article] A singular control problem with discretionary stopping for geometric Brownian motions2010

    • Author(s)
      H. Morimoto
    • Journal Title

      SIAM J. Control Optim

      Volume: 48 Pages: 3781-3804

  • [Journal Article] Optimal dividend payments in the stochastic Ramsey model2010

    • Author(s)
      H. Morimoto
    • Journal Title

      Stochastic Process. Appl

      Volume: 120 Pages: 427-441

  • [Journal Article] Optimal consumption of the finite time horizon Ramsey problem2009

    • Author(s)
      T. Adachi, H. Morimoto
    • Journal Title

      J. Math. Anal. Appl

      Volume: 358 Pages: 28-46

  • [Journal Article] An irreversible investment problem with maintenance expenditure

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

      SIAM J. Control Optim

      Volume: (印刷中)

  • [Journal Article] Optimal dividend and risk control in diffusion models with linear costs

    • Author(s)
      H. Morimoto
    • Journal Title

      OR2011 Proceedings

      Volume: (掲載予定)

  • [Presentation] Variational inequalities in the optimal dividend and risk control problem2012

    • Organizer
      環瀬戸内ワークショッップ
    • Place of Presentation
      愛媛大学
    • Year and Date
      20120200
  • [Presentation] Optimal dividend and risk control in diffusion models with linear costs2011

    • Organizer
      OR2011 Zurich
    • Place of Presentation
      University of Zurich
    • Year and Date
      20110800
  • [Presentation] Parabolic variational inequalities for optimal dividends in the logistic model2011

    • Organizer
      松山解析セミナー
    • Place of Presentation
      愛媛大学
    • Year and Date
      20110200
  • [Presentation] On the penalty method in an irreversible investment problem2010

    • Organizer
      微分方程式深江ワークショップ
    • Place of Presentation
      神戸大学
    • Year and Date
      20100100
  • [Presentation] 幾何ブラウン運動に対するsingular controlとoptimal stopping2009

    • Organizer
      確率論シンポジウム
    • Place of Presentation
      愛媛大学
    • Year and Date
      20091200
  • [Presentation] Variational inequalities with gradient constraint and applications to optimal dividend payments2009

    • Organizer
      微分方程式の粘性解とその周辺
    • Place of Presentation
      京都大学数理研
    • Year and Date
      20090600
  • [Book] Cambridge University Press2010

    • Author(s)
      H. Morimoto
    • Total Pages
      325
    • Publisher
      Stochastic Control and Mathematical Modeling : Applications in Economics

URL: 

Published: 2013-07-31  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi