Studies on nonlinear variational inequalities by viscosity solutions
Project/Area Number 
14540178

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Basic analysis

Research Institution  Ehime University 
Principal Investigator 
MORIMOTO Hiroaki Ehime Univ., Faculty of Science, Professor, 理学部, 教授 (80166438)

CoInvestigator(Kenkyūbuntansha) 
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)

Keywords  Variational 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 nonlinear 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 nonlinear variational inequalities is given. The penalty method for linear variational inequalities originated by BensoussanLions is developed, and it is shown that there exists a unique viscosity solution of the nonlinear variational inequality. The game problem in the same setting is discussed. (2) In the paper "Variational inequalities for leavable boundedvelocity control", the key for the smoothness problem of the viscosity solutions to nonlinear variational inequalities is presented. Recently, it becomes well known when the viscosity solutions of HamiltonJacobiBellman 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)
Research Products
(14 results)