Nonlinear stochastic and dynamic decision processes by invariantAnd imbedding methods

• Project/Area Number: 21540132
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kochi University
• Principal Investigator: OHTSUBO Yoshio 高知大学, 教育研究部自然科学系, 教授 (20136360)
• Co-Investigator(Kenkyū-buntansha): YASUDA Masami 千葉大学, 名誉教授 (00041244) ; YOSHIDA Yuji 北九州大学, 経済学部, 教授 (90192426)
• Co-Investigator(Renkei-kenkyūsha): NOMAKUCHI Kentarou 高知大学, 教育研究部自然科学系, 教授 (60124806) ; IWAMOTO Seiichi 九州大学, 名誉教授 (90037284)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 数理モデル / 計画数学 / マルコフ決定過程 / リスク最小化 / 動的計画 / ポートフォーリオ / 最適方程式 / フィボナッチ数列 / 強自動連続性 / 閾値確率 / 最適政策 / 零和停止ゲーム / セミマルコフ決定過程 / リスク最小化問題 / 零和ゲーム / 鞍部点 / 黄金最適性 / 黄金パス / 区間ベイズ手法

Research Abstract

We consider undiscounted semi-Markov decision process with a target set and our main concern is a problem minimizing threshold probability. We formulate the problem as an infinite horizon case with a recurrent class. We show that an optimal value function is a unique solution to an optimality equation and there exists a stationary optimal policy. Also several value iteration methods and a policy improvement method are given in our model. Furthermore, we investigate a relationship between threshold probabilities and expectations for total rewards.

Research Products

• [Journal Article] Weighted Quasi-Arithmetic Means and Domain Translations (2012)
  • Author(s): Yoshida Yuji
  • Journal Title: Journal of Advanced Computational Intelligence and Intelligent Informatics Volume: Vol.16, No.1 Pages: 148-153
  • Peer Reviewed
• [Journal Article] An Ordered Weighted Average with a Truncation Weight on Intervals in Lecture Notes in Artificial Intelligence (2012)
  • Author(s): Yoshida Yuji
  • Journal Title: Modeling Decisions for Artificial Intelligence - MDAI2012, edited by V.Torra and Y.Narukawa, Springer Volume: Vol.7647 Pages: 45-55
  • Peer Reviewed
• [Journal Article] Weighted Quasi-Arithmetic Means and Domain Translations (2012)
  • Author(s): Y.Yoshida
  • Journal Title: Journal of Advanced Computational Intelligence and Intelligent Volume: Vol.16, No.1 Pages: 148-153
  • Peer Reviewed
• [Journal Article] A Dynamic Risk Allocation of Value-at-Risks with Portfolios (2012)
  • Author(s): Y.Yoshida
  • Journal Title: Journal of Advanced Computational Intelligence and Intelligent Informatics Volume: Vol.16, No.7, Pages: 800-806
  • Peer Reviewed
• [Journal Article] An Ordered Weighted Average with a Truncation Weight on Intervals (2012)
  • Author(s): Y.Yoshida
  • Journal Title: Lecture Notes in Artificial Intelligence Volume: Vol.7647 Pages: 45-55
  • Peer Reviewed
• [Journal Article] ラグランジュ関数のフィボナッチ鞍点 (2012)
  • Author(s): 岩本誠一、木村 寛
  • Journal Title: 京大数理研講究録「不確実・不確定環境下における数理的意思決定とその周辺」、 Volume: No.1802 Pages: 50-56
• [Journal Article] 負のマルコフ決定過程における二つの閾値確率最適化の方法,数理解析研究所講究録 (2011)
  • Author(s): 阪口昌彦,大坪義夫
  • Journal Title: 最適化モデルとアルゴリズムの新展開 Volume: No.1726 Pages: 84-96
• [Journal Article] Autocountinuity from below of set functions and convergence in measure (2011)
  • Author(s): Li Jun, Ling Zhou, Yasuda Masami
  • Journal Title: Springer Pages: 77-83
• [Journal Article] A Dynamic Value-at-Risk Portfolio Model in Lecture Notes in Artificial Intelligence 6820 (2011)
  • Author(s): Yuji,Yoshida
  • Journal Title: Modeling Decisions for Artificial Intelligence -MDAI2011', edited by V.Torra, Y.Narukawa, J.Yin and J.Long, Springer Pages: 43-54
  • Peer Reviewed
• [Journal Article] 負のマルコフ決定過程における二つの閾値確率最適化の方法 (2011)
  • Author(s): 阪口昌彦, 大坪義夫
  • Journal Title: 数理解析研究所講究録「最適化モデルとアルゴリズムの新展開」 Volume: No.1726 Pages: 84-96
• [Journal Article] Autocountinuity from below of set functions and convergence in measure (2011)
  • Author(s): Jun Li, Masami Yasuda, Ling Zhou
  • Journal Title: Nonlinear Maths.for Uncertainty and its Appli., Advances in Intel.and Soft Computing, Springer Volume: Vol.100 Pages: 77-83
  • DOI: 10.1007/978-3-642-22833-9_9
  • ISBN: 9783642228322, 9783642228339
  • Peer Reviewed
• [Journal Article] A Dynamic Value-at-Risk Portfolio Model (2011)
  • Author(s): Yuji Yoshida
  • Journal Title: Lecture Notes in Artificial Intelligence, Springer Volume: 6820 Pages: 43-54
  • DOI: 10.1007/978-3-642-22589-5_6
  • ISBN: 9783642225888, 9783642225895
  • Peer Reviewed
• [Journal Article] Optimal threshold probability and expectation in semi-Markov decision processes (2010)
  • Author(s): Masahiko Sakaguchi, Yoshio Ohtsubo
  • Journal Title: Applied Mathematics and Computation Volume: Vol.216, No.10 Pages: 2947-2958
  • Peer Reviewed
• [Journal Article] Stochastic Control (2010)
  • Author(s): Chris Myers, Intech
  • Journal Title: Zero-sum stopping game associated with threshold probability Pages: 81-86
• [Journal Article] Quasi-Arithmetic Means and Ratios of an Interval induced from Weighted Aggregation Operations (2010)
  • Author(s): Yuji Yoshida
  • Journal Title: Soft Computing Volume: Vol.14, No.5 Pages: 473-485
  • Peer Reviewed
• [Journal Article] Modeling Decisions for Artificial Intelligence No.8211; MDAI2010 (2010)
  • Author(s): Yuji YoshidaV.Torra, Y.Narukawa and M.Daumas
  • Journal Title: Weighted quasi-arithmetic means and conditional expectations Lecture Notes in Artificial Intelligence 6408 Pages: 31-42
  • Peer Reviewed
• [Journal Article] An Average Value-at-Risk Portfolio Model under Uncertainty: A perception-Based Approach by Fuzzy Random Variables (2010)
  • Author(s): Yuji Yoshida
  • Journal Title: Journal of Advanced Computational Intelligence and Intelligent Informatics Volume: Vol.15, No.1 Pages: 56-62
  • Peer Reviewed
• [Journal Article] Zero-sum stopping game associated with threshold probability (2010)
  • Author(s): Yoshio Ohtsubo
  • Journal Title: "Stochastic Control", Edited by Chris Myers, Sciyo.com Pages: 81-86
• [Journal Article] Optimal threshold probability and policy iteration in semi-Markov decision processes (2010)
  • Author(s): Masahiko Sakaguchi
  • Journal Title: International J.of Pure and Applied Mathematics 59巻 Pages: 225-242
  • Peer Reviewed
• [Journal Article] Zero-sum stopping game associated with threshold probability (2010)
  • Author(s): Yoshio Ohtsubo
  • Journal Title: Stochastic Control, Sciyo.com (掲載確定)
• [Journal Article] Golden Optimal path in Discrete-time Dynamic Optimization Processes (2009)
  • Author(s): S.Iwamoto, Masami Yasuda
  • Journal Title: Advanced Studies in Pure Math Volume: Volume 53 Pages: 99-108
• [Journal Article] An Estimation Model of Value-at-Risk Portfolio under Uncertainty (2009)
  • Author(s): Yuji Yoshida
  • Journal Title: Fuzzy Sets and Systems Volume: Vol.160, No.22 Pages: 3250-3262
• [Journal Article] Modeling Decisions for Artificial Intelligence (2009)
  • Author(s): Yuji Yoshida
  • Journal Title: A Perception-Based Portfolio under Uncertainty: Minimization of Average Rates of Falling,Lecture Notes in Artificial Intelligence 5861 Volume: No.8211 Pages: 149-160
• [Journal Article] The best choice problem for random number of objects with a refusal probability (2009)
  • Author(s): M.Horiguchi, Masami, Yasuda
  • Journal Title: INFORMS Applied Probability, Draft Pages: 1-8
• [Journal Article] Golden Optimal path in Discrete-time Dynamic Optimization Processes (2009)
  • Author(s): Seiichi Iwamoto
  • Journal Title: Advanced Studies in Pure Math. 53 Pages: 99-108
  • Peer Reviewed
• [Presentation] Continuous-time linear-quadratic dynamic optimization evaluation/optimization and Bellman equation (2013)
  • Author(s): S.Iwamoto
  • Organizer: 京都大学数理解析研究所共同研究集会「マクロ経済動学と非線形解析」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2013-02-28
• [Presentation] An ordered weighted average with a truncation weight on intervals (2012)
  • Author(s): Yuji Yoshida
  • Organizer: 第9回人工知能の決定モデルに関する国際会議MDAI2012
  • Place of Presentation: Girona, Spain
  • Year and Date: 2012-11-21
• [Presentation] Multiple stopping odds problem in Markov-dependent trials (2012)
  • Author(s): K. Ano, N. Kakie, N. Miyoshi, M.Yasuda
  • Organizer: 6th european congress of mathematics
  • Place of Presentation: Krakow, Poland
  • Year and Date: 2012-07-05
• [Presentation] An ordered weighted average with a truncation weight on intervals (2012)
  • Author(s): Y.Yoshida
  • Organizer: 第９回人工知能の決定モデルに関する国際会議MDAI2012
  • Place of Presentation: Girona, Spain
• [Presentation] Threshold Probability and Expectation Criteria for Additive Reward System (2011)
  • Author(s): M. Sakaguchi, Y.Ohtsubo
  • Organizer: 19th Triennial Conference of IFORS2011 (Conference of the International Federation of Operational Research Societies)
  • Place of Presentation: Melbourne, Australia
  • Year and Date: 2011-07-15
• [Presentation] Threshold Probability and Expectation Criteria for Additive Reward System (2011)
  • Author(s): Masahiko Sakaguchi, Yoshio Ohtsubo
  • Organizer: IFORS2011 (Conference of the International Federation of Operational Research Societies)
  • Place of Presentation: Melbourne, Australia
  • Year and Date: 2011-07-15
• [Presentation] Optimal threshold probability and expectation in Markov decision processes (2010)
  • Author(s): 阪口昌彦,大坪義夫
  • Organizer: 日本数学学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-23
• [Presentation] Optimal threshold probability and expectation in Markov decision processes (2010)
  • Author(s): 阪口昌彦, 大坪義夫
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-23
• [Presentation] 負のマルコフ決定過程における二つの閾値確率最適化の方法 (2010)
  • Author(s): 阪口 昌彦,大坪 義夫
  • Organizer: 研究集会「最適化モデルとアルゴリズムの新展開」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-07-22
• [Presentation] The best choice problem for random number of objects with a refusal probability (2009)
  • Author(s): Masami Yasuda
  • Organizer: INFORMS Applied Probability
  • Place of Presentation: Cornel Univ., USA
• [Remarks]
  • URL: http://www.math.s.chiba-u.ac.jp/~yasuda/