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

Studies on non-linear variational inequalities by viscosity solutions

Research Project

Project/Area Number 14540178
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  Ehime Univ., Faculty of Science, Professor, 理学部, 教授 (80166438)

Co-Investigator(Kenkyū-buntansha) ISHIKAWA Yasushi  Ehime Univ., Faculty of Science, Associate Professor, 理学部, 助教授 (70202976)
KAWAGUCHI Kazuhito  Ehime Univ., Faculty of Law and Letters, Associate Professor, 法文学部, 助教授 (30234040)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsVariational inequality / viscosity solution / stochastic control / 確立制御 / 非線形変分不等式 / 確率微分方程式 / 最適化
Research Abstract

The purpose of this study is to solve optimization problems in mathematical economics and mathematical finance by applications of the modern theory in stochastic control The main result in this term lies in opening up a field of research of non-linear variational inequalities for the problem so as to minimize the cost functional with discretionary stopping. The content is as follows.
(1)In the paper "Variational inequalities for combined control and stopping, 2003", the new definition of viscosity solutions for non-linear variational inequalities is given. The penalty method for linear variational inequalities originated by Bensoussan-Lions is developed, and it is shown that there exists a unique viscosity solution of the non-linear variational inequality. The game problem in the same setting is discussed.
(2) In the paper "Variational inequalities for leavable bounded-velocity control", the key for the smoothness problem of the viscosity solutions to non-linear variational inequalities is presented. Recently, it becomes well known when the viscosity solutions of Hamilton-Jacobi-Bellman equations are smooth for the construction of optimal policies. The paper "Optimal exploitation of renewable resources by the viscosity solution method" shows that the similar method is valid for the optimal consumption problem of renewable resources in mathematical economics. These results can be applicable for various optimization problems in future.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] K.Kamizono, H.Morimoto: "On a variational inequality associated with a stopping game combined with a control"Stoch.Stoch.Rep.. 73. 99-123 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Morimoto, K.Kawaguchi: "Optimal exploitation of renewable resources by the viscosity solution method"Stoch.Anal.Appl.. 20. 927-946 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Koike, H.Morimoto: "Variational inequalities for leavable bounded-velocity control"Appl.Math.Optim.. 48. 1-20 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Morimoto: "Variational inequalities for combined control with stopping"SIAM J.Control Optim.. 42. 686-708 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Kamizono, H.Morimoto: "On a variational inequality associated with a stopping game combined with a control"Stoch. Stoch. Rep.. 73. 99-123 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Morimoto, K.Kawaguchi: "Optimal exploitation of renewable resources by the viscosity solution method"Stoch. Anal. Appi.. 20. 927-946 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Koike, H.Morimoto: "Variational inequalities for leavable bounded-velocity control"Appl. Math. Optim.. 48. 1-20 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Morimoto: "Variational inequalities for combined control and stopping"SIAM J. Control Optim.. 42. 686-708 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Koike, H.Morimoto: "Variational inequalities for leavable bounded-velocity control"Appl.Math.Optim.. 48. 1-20 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Morimoto: "Variational inequalities for combined control and stopping"SIAM J.Control.Optim.. 42. 686-708 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Morimoto: "Variational inequalities for comfined control and stopping"SIAM J. Control and Optim. (掲載予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] Kamizono, K., Morimoto, H.: "On a variational inequality associated with a stopping game combined with a control"Stochastics and Stochastisc Rep.. 70. 99-123 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Morimoto, K.Kawaguchi: "Optimal exploitation of renewable resources by the viscosity solution method"Stoch. Anal. Appl.. 20. 927-946 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Koike, H.Morimoto: "On variational inequalities for leavable bounded-velocity control"Appl. Math. Optim.. (掲載予定).

    • Related Report
      2002 Annual Research Report

URL: 

Published: 2002-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi