Advances in stochastic optimization and derivatives pricing in financial engineering

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K01683
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 07060:Money and finance-related
• Research Institution: Kyoto University
• Principal Investigator: Egami Masahiko 京都大学, 経済学研究科, 教授 (40467395)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: マルコフ過程 / 拡散過程 / 最適停止問題 / 最終通過時刻 / 時間反転 / レジームスイッチ / CATボンド

Outline of Final Research Achievements

The main objectives include to study Markov processes, especially diffusions, in more a refined manner in view of explicitly solving problems which would not be handled otherwise, and to expand the range of solvable problems in finance by developing techniques commonly employable to general Markov processes, and to obtain new insights into results of model-based analyses by adding new prospective and through sophistication. The results include the following: we have solved optimal stopping problems under regime-switch models, advanced credit risk management by using time reversal techniques, and estimated the loss-given-default distribution. The first two projects successfully resulted in the publication at prestigious international journals.

Free Research Field

ファイナンス工学

Academic Significance and Societal Importance of the Research Achievements

対象とする確率過程そのものの性質を明らかにして利用することにより、特殊なケースだけでなく一般的なレベルで、最適化問題や価格付け問題の解法を可能にした。場合によっては明示解を求めることができるため学術的意義がある。同時に、解法可能な問題の範囲を拡大することができ、明示解は比較静学を容易にするため実務上有益な問題に関して、より正確な経済学的な知見を得ることに繋がる点で社会的意義がある。