Optimization in stochastic systems and applications to consumption problems

随机系统优化及其在消耗问题中的应用

• 批准号: 11640126
• 负责人: MORIMOTO Hiroaki
• 金额: $ 1.34万
• 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: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640126/
• 关键词: Stochastic Control; Stochastic differential equation; Hamilton-Jacobi-Bellman; consumption; Investment; Optimization; 確率過程; 粘性解; 非線形偏微分方程式

The objective is to study the optimization problems in Mathematical Economics and Mathematical Finance by the recent theory of stochastic control. The main interest lies in finding the solutions of non-linear differential equations called the Hamilton-Jacobi-Bellman equations. It is proved that these equations admit the classical solutions by using the viscosity solution method. The optimal policies are shown to exist and given from the optimality conditions of the equations. The research results supported by this grant can be stated in the following summaries of three articles below.1 : We study the ergodic control problem of production planning in stochastic manufacturing systems with constant demand. The optimal control and the minimum value are given by a solution to the corresponding Bellman equation.2 : We study consumption/investment problems with long-term time-average utilities. The associated Hamilton-Jacobi-Bellman equation can be solved under some regularity conditions of utility-rate function, and the optimal portfolio and consumption-rates are exhibited in explicit forms. An application to the optimization problem with finite horizon is also given.3 : We study the stochastic optimization problem of renewable resources to maximize the expected discounted utility of exploitation. The optimal policy is shown to exist and given in a feedback form or a stochastic version of Hotelling's rule.

目的是通过最新的随机控制理论研究数学经济学和数学金融中的优化问题。主要兴趣在于找到称为Hamilton-Jacobi-Bellman方程的非线性微分方程的解决方案。证明这些方程使用粘度解决方案方法接受了经典的解决方案。最佳策略显示出存在并根据方程式的最佳条件给出。该赠款支持的研究结果可以在以下三篇文章的摘要中说明。1：我们研究了需求持续需求的随机制造系统中生产计划的ergodic控制问题。最佳控制和最低值是通过对相应的贝尔曼方程的解决方案给出的。2：我们研究长期时间平均公用事业的消费/投资问题。相关的Hamilton-Jacobi-Bellman方程可以在某些规律性的效用函数条件下解决，并且最佳投资组合和消费率以明确的形式展示。 3：我们研究了可再生资源的随机优化问题，以最大程度地提高预期的剥削效用。最佳策略显示出存在并以反馈形式或Hotelling规则的随机版本给出。

项目成果

Y.fujita and H.Morimoto: "On Bellman equations in quadratic ergodic control with controller constraints"Appl.Math.Optim.. 39. 1-15 (1999)

Y.fujita 和 H.Morimoto：“关于具有控制器约束的二次遍历控制中的贝尔曼方程”Appl.Math.Optim.. 39. 1-15 (1999)

T.Adachi and H.Morimoto: "On consumption/investment problems with long-term time-average inequalities"Stoch.Stoch.Rep.. 68. 255-271 (2000)

T.Adachi 和 H.Morimoto：“论长期平均不平等的消费/投资问题”Stoch.Stoch.Rep.. 68. 255-271 (2000)

H,Morimoto and Y.Fujita: "Ergodic centrol in stochastic manufacturing systems with constant demand"J,Math,Anal,Appl,. 243. 228-248 (2000)

H，Morimoto 和 Y.Fujita：“具有恒定需求的随机制造系统中的遍历中心”J，Math，Anal，Appl，。

H.Morimoto and Y.Fujita: "Ergodec control in stockastic manufacturing systems with constant demand"J.Math.A;nal.Appl. (in press).

H.Morimoto 和 Y.Fujita：“具有恒定需求的库存制造系统中的 Ergodec 控制”J.Math.A；nal.Appl。

H.Morimoto and Y.Fujita: "Ergodic control in stochastic manufacturing systems with constant demand"J.Math.Anal.Appl.. 243. 228-248 (2000)

H.Morimoto 和 Y.Fujita：“具有恒定需求的随机制造系统中的遍历控制”J.Math.Anal.Appl.. 243. 228-248 (2000)