A Stochastic Approach to Capacity Choice Problems with the Planar Impulse Control

• Project/Area Number: 15K16290
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Social systems engineering/Safety system
• Research Institution: Hokkaido University
• Principal Investigator: Goto Makoto 北海道大学, 経済学研究院, 准教授 (30434286)
• Project Period (FY): 2015-04-01 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: リアルオプション / 設備投資 / インパルス制御 / スイッチング制御 / 環境投資 / 競争投資 / コーポレートファイナンス

Outline of Final Research Achievements

This research proposes a new stochastic control approach to the capacity choice problem. In particular, we have developed the new solution method named "Planar Impulse Control" that has 2 state variables. Our main results are as follows: (1) More efficient calculation methods of Planar Impulse Control; (2) an application to the corporate finance problem; (3) an application to the environmental investment problem; (4) an application to the competitive investment problem.

Academic Significance and Societal Importance of the Research Achievements

本研究から得られる解は，経済全体の波及効果のようなマクロ的視点とは根本的に異なり，個々の企業がどのようなタイミングで設備投資をするかという戦略である．これによって，減税や規制緩和による個々の企業の最適行動の変化が分析可能になり，成長戦略の分析にミクロ的視点を加えることが可能になる．また，本研究の手順は他の問題へも応用可能である．特に，コーポレート・ファイナンスのキャッシュリザーブ問題はインパルス制御による分析が可能であり，応用が実現できれば，金融システムの安定化という国際的に重要視されている問題の解決への手掛かりとなり得る．

Research Products

• [Journal Article] リアルオプションの確率モデル (2017)
  • Author(s): 後藤允
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 2029 Pages: 21-28
• [Journal Article] 四則演算によるリアルオプション (2017)
  • Author(s): 後藤允
  • Journal Title: リアルオプションと戦略 Volume: 9(1) Pages: 44-50
  • NAID: 130007584658
• [Journal Article] Leaders, Followers, and Equity Risk Premium in Booms and Busts (2016)
  • Author(s): Makoto, Goto, Katsumasa, Nishide, Ryuta Takashima
  • Journal Title: Journal of Banking & Finance Volume: Available online 10 October Pages: 1-14
  • DOI: 10.1016/j.jbankfin.2016.08.010
  • NAID: 120006876266
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Pollution Thresholds under Uncertainty in Asymmetric Duopoly (2016)
  • Author(s): Goto, M., Takashima, R. and Tsujimura, M.
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1983 Pages: 27-40
  • Acknowledgement Compliant
• [Journal Article] A Model of Purchase Behavior under Price Uncertainty: A Real Options Approach (2015)
  • Author(s): Suzuki, H., Goto, M. and Ohno, T
  • Journal Title: International Journal of Real Options and Strategy Volume: 3 Issue: 0 Pages: 1-12
  • DOI: 10.12949/ijros.3.1
  • NAID: 130005117923
  • ISSN: 2186-4667
  • Peer Reviewed / Open Access
• [Journal Article] Optimal Default and Liquidation with Tangible Assets and Debt Renegotiation (2015)
  • Author(s): Goto, M. and Suzuki, T.
  • Journal Title: Review of Financial Economics Volume: 27 Issue: 1 Pages: 16-27
  • DOI: 10.1016/j.rfe.2015.07.001
  • Peer Reviewed
• [Journal Article] An Evaluation Model for Introducing the RVM Effect for Plastic Bottle Recycling Firms (2015)
  • Author(s): 鈴木広人, 後藤允, 大野高裕
  • Journal Title: Journal of Japan Industrial Management Association Volume: 66 Issue: 3 Pages: 287-299
  • DOI: 10.11221/jima.66.287
  • NAID: 130005107069
  • ISSN: 1342-2618, 2187-9079
  • Peer Reviewed / Open Access
• [Presentation] Policy Decisions and Social Welfare in Renewable Portfolio Standards (2018)
  • Author(s): Goto, M. and Takashima, R.
  • Organizer: INFORMS Annual Meeting 2018
  • Int'l Joint Research
• [Presentation] A Note on Impulse Control with Outside Jumps (2018)
  • Author(s): 後藤允, 金川聖也
  • Organizer: 平成30年度数理解析研究所共同研究（公開型）, ファイナンスの数理解析とその応用
• [Presentation] Policy Decisions and Social Welfare in Renewable Portfolio Standards (2018)
  • Author(s): 後藤允, 高嶋隆太
  • Organizer: 平成30年度数理解析研究所共同研究（公開型）, ファイナンスの数理解析とその応用
• [Presentation] A Note on Impulse Control with Outside Jumps (2018)
  • Author(s): Goto, M. and Kanagawa, S.
  • Organizer: ENRE and SOLA Joint Seminar 2018
• [Presentation] Real Options in Renewable Portfolio Standards (2017)
  • Author(s): 後藤允, 高嶋隆太
  • Organizer: 日本リアルオプション学会2017年研究発表大会
• [Presentation] Real Options in Renewable Portfolio Standards (2017)
  • Author(s): 後藤允, 高嶋隆太
  • Organizer: 平成29年度数理解析研究所共同研究（公開型）, ファイナンスの数理解析とその応用
• [Presentation] Real Options in Renewable Portfolio Standards (2017)
  • Author(s): 後藤允, 高嶋隆太
  • Organizer: 日本オペレーションズ・リサーチ学会2017年秋季研究発表会
• [Presentation] Real Options in Renewable Portfolio Standards (2017)
  • Author(s): Goto, M. and Takashima, R.
  • Organizer: 21st Conference of the International Federation of Operational Research Societies
  • Int'l Joint Research
• [Presentation] チュートリアル:リアルオプションの確率モデル (2016)
  • Author(s): 後藤允
  • Organizer: 平成28年度数理解析研究所研究集会
  • Place of Presentation: 京都大学（京都）
  • Year and Date: 2016-11-29
  • Invited
• [Presentation] チュートリアル:四則演算によるリアルオプション (2016)
  • Author(s): 後藤允
  • Organizer: 日本リアルオプション学会2016年研究発表大会
  • Place of Presentation: 中央大学（東京）
  • Year and Date: 2016-11-20
  • Invited
• [Presentation] Real Options in Renewable Portfolio Standards (2016)
  • Author(s): Takashima, R. and Goto, M.
  • Organizer: INFORMS Annual Meeting 2016
  • Place of Presentation: Music City Center (Nashville)
  • Year and Date: 2016-11-13
  • Int'l Joint Research
• [Presentation] The Effect of Environmental Regulation on Strategic Decision (2016)
  • Author(s): 後藤允, 高嶋隆太, 辻村元男
  • Organizer: 日本オペレーションズ・リサーチ学会2016年秋季研究発表会
  • Place of Presentation: 山形大学（山形）
  • Year and Date: 2016-09-15
• [Presentation] Environmental Regulation and Entry-Exit Decisions (2016)
  • Author(s): Goto, M., Takashima, R. and Tsujimura, M.
  • Organizer: 20th Annual International Real Options Conference
  • Place of Presentation: University of Oslo (Oslo)
  • Year and Date: 2016-06-16
  • Int'l Joint Research
• [Presentation] Introduction to Real Option Analysis Part I-III (2016)
  • Author(s): Goto, M.
  • Organizer: Winter Workshop on Operations Research, Finance and Mathematics, 2015
  • Place of Presentation: サホロリゾートホテル（夕張市）
  • Year and Date: 2016-02-17
  • Int'l Joint Research / Invited
• [Presentation] Pollution Thresholds under Uncertainty in Asymmetric Duopoly (2015)
  • Author(s): 後藤允, 高嶋隆太, 辻村元男
  • Organizer: 平成27年度数理解析研究所研究集会, ファイナンスの数理解析とその応用
  • Place of Presentation: 京都大学（京都市）
  • Year and Date: 2015-11-16
• [Presentation] A Model of Purchase Behavior under Price Uncertainty: A Real Options Approach (2015)
  • Author(s): 鈴木広人, 後藤允, 大野高裕
  • Organizer: 日本リアルオプション学会2015年研究発表大会
  • Place of Presentation: 国際大学（南魚沼市）
  • Year and Date: 2015-10-25
• [Presentation] On the Impulse Control Problem with Outside Jumps (2015)
  • Author(s): Goto, M.
  • Organizer: 5th International IMS-FIPS Workshop
  • Place of Presentation: Rutgers University (New Brunswick)
  • Year and Date: 2015-06-26
  • Int'l Joint Research
• [Remarks] 北海道大学研究者総覧
  • URL: https://researchers.general.hokudai.ac.jp/profile/ja.RpPTXxNY.pEWe3fjMQOADg==.html
• [Remarks] 北海道大学研究者総覧
  • URL: http://researchers.general.hokudai.ac.jp/profile/ja.RpPTXxNY.pEWe3fjMQOADg==.html