Study of risk-averse limits in stochastic control and robust models

• Project/Area Number: 25400137
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Osaka University
• Principal Investigator: Kaise Hidehiro 大阪大学, 基礎工学研究科, 准教授 (60377778)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 確率制御 / 確率論 / 数理ファイナンス / 動的計画偏微分方程式 / 粘性解 / 動的計画法 / HJB偏微分方程式

Outline of Final Research Achievements

Robust models to uncertainty such as noises in systems attract a lot of attentions in theories and applications. In this project, we considered risk-averse limits of problems in mathematical finance and their generalizations of stochastic controls. We succeeded in deriving robust models and developing dynamic programming methods. We also studied optimal control problems for path-dependent systems related to robust models.

Research Products

• [Journal Article] Path-dependent differential games of inf-sup type and Isaacs partial differential equations (2015)
  • Author(s): H. Kaise
  • Journal Title: IEEE 54th Conference on Decision and Control Volume: 1 Pages: 1972-1977
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] $H^\infty$-control model for a partially observed optimal investment problem (2014)
  • Author(s): H. Kaise
  • Journal Title: Proceedings of 21st International Symposium on Mathematical Theory of Networks and Systems Volume: 1 Pages: 158-165
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Path-dependent differential games of inf-sup type and dynamic programming equations (2016)
  • Author(s): H. Kaise
  • Organizer: Seminar on problems under model uncertainty and related topics motivated by mathematical finance
  • Place of Presentation: 大阪大学（大阪府豊中市）
  • Year and Date: 2016-02-25
  • Int'l Joint Research / Invited
• [Presentation] Path-dependent differential games of inf-sup type and Isaacs partial differential equations (2015)
  • Author(s): H. Kaise
  • Organizer: 54th IEEE Conference on Decision and Control
  • Place of Presentation: 大阪府立国際会議場（大阪府大阪市）
  • Year and Date: 2015-12-15
  • Int'l Joint Research
• [Presentation] Convergence of discrete-time deterministic games to path-dependent Isaacs partial differential equations (2015)
  • Author(s): 貝瀬秀裕
  • Organizer: 第５回数理ファイナンス合宿型セミナー
  • Place of Presentation: クロスウェーブ府中（東京都府中市）
  • Year and Date: 2015-11-06
  • Invited
• [Presentation] Dynamic programing for path-dependent deterministic control and idempotent expansion methods (2015)
  • Author(s): H. Kaise
  • Organizer: SIAM Conference on Control & its Applications
  • Place of Presentation: Paris, France
  • Year and Date: 2015-07-08
  • Int'l Joint Research / Invited
• [Presentation] $H^\infty$-control model for a partially observed optimal investment problem (2014)
  • Author(s): H. Kaise
  • Organizer: 21st International Symposium on Mathematical Theory of Networks and Systems
  • Place of Presentation: University of Groningen, The Netherland
  • Year and Date: 2014-07-07
• [Presentation] Risk-averse limits in finance aplications
  • Author(s): H. Kaise
  • Organizer: SIAM Conference on Control and its Applications
  • Place of Presentation: San Diego, USA
• [Presentation] Dynamic importance sampling for path-dependent events: path-dependent dynamic programming method
  • Author(s): 貝瀬秀裕
  • Organizer: 金融リスクの計測・管理・制御と資本に纏わる諸問題
  • Place of Presentation: 大阪大学
  • Invited