Nonlinear dynamic optimization theory on stochastic model and its application to mathematical finance
| Project/Area Number |
17540121
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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 | Kochi University |
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Principal Investigator |
OHTSUBO Yoshio Kochi University, Faculty of Science, Professor (20136360)
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| Co-Investigator(Kenkyū-buntansha) |
YASUDA Masami Chiba University, Faculty of Science, Professor (00041244)
IWAMOTO Seiichi Kyushu University, Faculty of Economics, Professor (90037284)
NOMAKUCHI Kentaro KOCHI UNIVERSITY, Faculty of Science, Professor (60124806)
新関 章三 高知大学, 理学部, 教授 (60036572)
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| Project Period (FY) |
2005 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | nonlinear criteria / optimization theory / Markov decision process / Fuzzy decision process / dynamic programming / shortest path problem / statistical inference / Golden ratio / 結合型評価関数 / 学習アルゴリズム / 不偏推定 / ミニマム型評価関数 / 効用制約決定過程 / 鞍点定理 / 測度空間 / アメリカン・オプショシ / 動的ファジイシステム / 集合列の収束 / EMアルゴリズム |
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| Research Abstract |
The summary of research results is as follows.
1. We consider multistage decision processes where a criterion function is an expectation of minimum function and formulate it as Markov decision processes with imbedded parameters. The policy depends upon a history including past imbedded parameters and the rewards at each stage is random and depends upon a current state, a current action and a next state. We give an optimality equation by using operators and show that there exist a right continuous deterministic Markov policy which depend upon a current state and an imbedded parameter.
2. We consider Markov decisions processes with a target set, where criterion function is an expectation of minimum function. We formulate the problem as an infinite horizon case with a recurrent class. We show under some conditions that an optimal value function is a unique solution to an optimality equation and there exists an stationary optimal policy. Also we give a policy improvement method.
3. We conside
… More
r a stochastic shortest path problem with associative criteria in which for each node of a graph we choose a probability distribution over the set of successor nodes so as to reach a given target node optimally. We formulate such a problem as an associative Markov decision processes. We show that an optimal value function is a unique solution to an optimality equation and find an optimal stationary policy. Also we give a value iteration method and a policy improvement method.
4. We consider utility-constrained Markov decision processes. The expected utility of the total discounted reward is maximized subject to multiple expected utility constraints. By introducing a corresponding Lagrange function, saddle-point theorem of the utility constrained optimization is derived. The existence of a constrained optimal policy is characterized by optimal action sets specified with a parametric utility.
5. We consider an inequality condition where one side is greater than or equal to a multiple of the other side and an equality holds if and only if one value is a multiple of the other variable. We show a cross-duality between four pairs of Golden inequalities for one-variable functions. Less
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Report
(4 results)
Research Products
(65 results)
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[Journal Article] 動学的最適化における黄金最適政策2007
Author(s)
S. Iwamoto
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Journal Title
小特集:経済分析と最適化の数理, 『三田学会雑誌』(慶應義塾経済学会) 99巻4号,
Pages: 101-125
NAID
Description
「研究成果報告書概要(和文)」より
Related Report
Peer Reviewed
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