Theory of viscosity solutions for nonlinear variational inequalities and its applications

非线性变分不等式的粘度解理论及其应用

• 批准号: 21540188
• 负责人: MORIMOTO Hiroaki
• 金额: $ 2万
• 依托单位: Ehime University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540188/
• 关键词: 変分不等式; 粘性解; penalty法; 幾何ブラウン運動; 確率制御

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 bookThis book provides the mathematical foundation for broader applications to mathematical economics.(2) Development of the penalty methodThe penalty equations are developed to solve nonlinear variational inequalities with gradient constraint.

研究了数理经济学中的随机微分方程描述的状态效用函数最大化的优化问题和非线性变分不等式问题。（1）出版了《数理经济学》一书，为数理经济学的广泛应用奠定了数学基础。(2)罚函数法的发展建立了求解带梯度约束的非线性变分不等式的罚函数方程。

项目成果

An Irreversible Investment Problem with Maintenance Expenditure

• DOI: 10.1137/100799484
• 发表时间: 2012-05
• 期刊: SIAM J. Control. Optim.
• 作者: Kazuhito Kawaguchi;H. Morimoto

Cambridge University Press

• DOI: 10.1163/_afco_asc_2206
• 发表时间: 2021-06
• 作者: Cambridge University Press

Optimal dividend payments in the stochastic Ramsey model

• DOI: 10.1016/j.spa.2010.01.001
• 发表时间: 2010-04
• 期刊: Stochastic Processes and their Applications
• 影响因子: 1.4
• 作者: H. Morimoto

A singular control problem with discretionary stopping for geometric Brownian motions

几何布朗运动任意停止的奇异控制问题

• 发表时间: 2010
• 期刊: SIAM J. Control Optim
• 作者: Alexandrova;Ivana and Tamura;Hideo;田島慎一;H. Morimoto
• 通讯作者: H. Morimoto

Optimal dividend and risk control in diffusion models with linear costs

具有线性成本的扩散模型中的最优股息和风险控制

• 期刊: OR2011 Proceedings
• 作者: Iwatsuka;Akira and Mine;Takuya and Shimada;Shin-ichi;H. Morimoto
• 通讯作者: H. Morimoto