Optimization in stochastic systems and applications to consumption problems
Project/Area Number 
11640126

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

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

CoInvestigator(Kenkyūbuntansha) 
ISHIKAWA Yasushi Ehime University, Faculty of Science, Associate Professor, 理学部, 助教授 (70202976)
YANAGI Shigenori Ehime University, Faculty of Science, Associate Professor, 理学部, 助教授 (10253296)
KAWAGUCHI Kazuhito Ehime University, Faculty of Law and Letters, Associate Professor, 法文学部, 助教授 (30234040)

Project Period (FY) 
1999 – 2000

Project Status 
Completed (Fiscal Year 2000)

Budget Amount *help 
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2000: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1999: ¥1,200,000 (Direct Cost: ¥1,200,000)

Keywords  Stochastic Control / Stochastic differential equation / HamiltonJacobiBellman / consumption / Investment / Optimization / 確率過程 / 粘性解 / 非線形偏微分方程式 
Research Abstract 
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 nonlinear differential equations called the HamiltonJacobiBellman 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 longterm timeaverage utilities. The associated HamiltonJacobiBellman equation can be solved under some regularity conditions of utilityrate function, and the optimal portfolio and consumptionrates 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.

Report
(3 results)
Research Products
(14 results)