2013 Fiscal Year Final Research Report
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 |
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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 | Kyushu University |
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Principal Investigator |
IWAMOTO Seiichi 九州大学, 経済学研究科(研究院), 名誉教授 (90037284)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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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 |
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| 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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