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Studies on Dynamic Optimization of Stochastic Systems with Multiple Criteria

Research Project

Project/Area Number 10680427
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 社会システム工学
Research InstitutionOsaka University

Principal Investigator

OHNISHI Masamitsu  Associate Professor, Graduate School of Economics Osaka University, 大学院・経済学研究科, 助教授 (10160566)

Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2000: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1999: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1998: ¥1,900,000 (Direct Cost: ¥1,900,000)
KeywordsOptimal stopping problem / Poisson process / Geometric Brownian motion / Smooth pasting / Impulse control / Risk aversion / Stochastic dominance / Multiple criteria Markov decision process / 拡散過程 / 配当政策 / キャッシュ・マネージメント / 確率優位(確率順序) / 信頼性・保全性 / 投資意思決定 / マルチンゲール
Research Abstract

First, I examined an optimal stopping problem for a geometric Brownian motion with Poissonian jumps. Although it has been argued that so called smooth pasting technique (see Dixit (1993), and Dixit and Pindyck (1994)) is useful for such stochastic optimization problems, it seems that its mathematical validity is not sufficiently discussed so far. In this project, by taking a martingale approach, I showed that it is indeed mathematically valid under a set of some mild conditions on the parameters of the problem.
Stochastic dominances (stochastic orders) and inequalities are very useful tools in various areas of economics and finance. The second purpose of this project was to describe main results obtained so far by using the idea of stochastic dominances in financial optimization. Especially, the emphasis is placed on the demand and shift effect problems in portfolio selection. Some other examples, which are not related directly to optimization problems, are also gathered to demonstrate the wide spectrum of application areas of stochastic dominances in finance. Further, since several stochastic dominances and related inequalities which are known in the reliability and maintainability theory, are very useful even in finance theory, the next purpose of this project was to provide a brief survey of the useful known results concerning stochastic orders and their applications developed in various areas of the reliability and maintainability theory.

Report

(4 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (20 results)

All Other

All Publications (20 results)

  • [Publications] Ohnishi,M.: "An Optimal Stopping Problem for a Geometric Brownian Motion with Poissonian Jumps"Proceedings of the First Euro-Japanese Workshop on Risk Modelling for Finance, Insurance, Production and Reliability. 1. (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Ohnishi,M.: "An Optimal Stopping Problem for a Geometric Brownian Motion with Poissonian Jumps"Stochastic Models in Engineering Technology and Management (Wilson, R.J.,Osaki,S.and Faddy,M.J.Eds.). 416-425 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Kijima,M.and Ohnishi,M.: "Stochastic Orders and Their Applications in Financial Optimization"Mathematical Methods of Operations Research. 50. 351-372 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Segawa,Y.and Ohnishi,M: "The Average Optimality of a Repair-Limit Replacement Policy"Mathematical and Computer Modelling. 31. 327-334 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Ohnishi,M.: "Stochastic Orders in Reliability Theory"Stochastic Models in Reliability and Maintenance (Osaki,S.Ed.), Chap.1, Springer-Verlag, Berlin. (in press). (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 大西匡光 (分担訳): "経営科学OR用語大事典"朝倉書店. 760 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 大西匡光 (部分執筆): "経営学大辞典(第2版)"中央経済社. 1048 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Ohnishi, M.: "An Optimal Stopping Problem for a Geometric Brownian Motion with Poissonian Jumps"Proceedings of the First Euro-Japanese Workshop on Risk Modelling for Finance, Insurance, Production and Reliability. Vol.1. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Ohnishi, M.: "An Optimal Stopping Problem for a Geometric Brownian Motion with Poissonian Jumps"Stochastic Models in Engineering, Technology and Management (Wilson, R.J., Osaki, S.and Faddy, M.J.Eds.). 416-425 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Kijima, M.and Ohnishi, M.: "Stochastic Orders and Their Applications in Financial Optimization"Mathematical Methods of Operations Research. Vol.50. 351-372 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Segawa, Y.and Ohnishi, M.: "The Average Optimality of a Repair-Limit Replacement Policy"Mathematical and Computer Modelling. Vol.31. 327-334 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Ohnishi, M.: "Stochastic Orders in Reliability Theory"Stochastic Models in Reliability and Maintenance (Osaki, S.Ed.), Chap.1, Springer-Verlag, Berlin (in press). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Segawa,Y.and Ohnishi,M: "The Average Optimality of a Repair-Limit Replacement Policy"Mathematical and Computer Modelling. 31. 327-334 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Ohnishi,M.: "Stochastic Orders in Reliability Theory"Stochastic Models in Reliability and Maintenance (Osaki,S.Ed.), Chap.1, Springer-Verlag, Berlin. (forthcoming). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] Ohnisi M.: "An Optimal Stopping Problem for a Geometric Brownian Motion with Poissonian Jumps"Stochastic Models in Engineering, Technology and Management (Wilson, R.J., Osaki, S. and Faddy, M.J. Ed). 416-425 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Kijima M.and Ohnisi M.: "Stochastic Orders and Their Applications in Financial Optimization"Mathematical Methods of Operations Research. 50. 351-372 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 大西匡光(部分執筆): "経営学大辞典"中央経済社(第2版). 1048 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Ohnishi,M.: "An Optimal Stopping Problem for Geometric Brownian Motion with Poissonian Jumps" Proceedings of the First Euro-Japanese Workshop on Risk Modelling for Finance,Insurance,Production and Rebability. 1. (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Segawa,Y.and Ohnishi,M.: "On The Average Optimality of a Repait-Limit Replacement Policy" Mathematical & Compuer Modelling. (in press). (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 大西匡光分担訳: "経営科学 OR 用語大事典" 朝倉書店, 760 (1999)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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