| Project/Area Number |
11640126
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ehime University |
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Principal Investigator |
MORIMOTO Hiroaki Ehime University, Faculty of Science, Professor, 理学部, 教授 (80166438)
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| Co-Investigator(Kenkyū-buntansha) |
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)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| 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)
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| Keywords | 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 |
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| 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 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.
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