An inclusive study of Bellman equation in dynamic programming and applications to mathematical economics
Project/Area Number |
22540144
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Kyushu University |
Principal Investigator |
IWAMOTO Seiichi 九州大学, 経済学研究科(研究院), 名誉教授 (90037284)
|
Project Period (FY) |
2010-04-01 – 2014-03-31
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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Keywords | 動的計画法 / ベルマン方程式 / 双対方程式 / 双対最適化問題 / 動的双対 / フェンシェル双対 / フィボナッチ双対 / 黄金双対 / フィボナッチ最適 / 黄金最適 / パラメトリック計画 / 分数計画 / フィボナナッチ双対 / オイラー方程式 / 変分法 / 不等式による接近 / フィボナッチ相補双対 / 黄金シフト双対 / 黄金最適政策 / マックス関数方程式 / 零和解 / 単位積解 / 黄金経路 / フィボナッチ経路 |
Research Abstract |
This research investigates an analytic solution of Bellman equation in dynamic programming and applies it to mathematical economics. The Bellman equation governs an optimal behavior of an asssociated dynamic optimization problem. A desired optimal solution of the optimization problem is characterized through optimal solution of the Bellman equation, which consists of a pair of optimal policy and optimal value function. We derive a dual equation from a given (primal) Bellman euation, which yields a dual dynamic optimization problem of a given (primal) problem. Optimal solutions of the two problems are obtained by solving the corresponding Bellman equations. The dual theory is applied to economic growth model in economic dynamics.
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Report
(5 results)
Research Products
(41 results)