2016 Fiscal Year Final Research Report
Construction and Applications of risk measure theory based on category theory
| Project/Area Number |
26330026
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical informatics
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| Research Institution | Hitotsubashi University |
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Principal Investigator |
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| Research Collaborator |
TAKADA Hideyuki
YAMANAKA Suguru
KENMOTSU Teruo
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 金融リスク / 圏論 |
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| Outline of Final Research Achievements |
We reviewed financial risk measures in line with the abstract mathematical framework of `category theory' which has never used in traditional finance research, we succeeded in introducing the category `Prob', which has all probability spaces as the objects. This category has a very high generality so as to not only analyze stochastic-jump models for credit risk events but apply to many other research fields.
In addition, from the viewpoint of application to credit risk, especially corporate bankruptcy concentration risk, we studied some new estimation methods of self-exciting effects and mutually-exciting effects of intensity of credit event occurrence such as bankruptcy, as well as a method of bankruptcy probability estimation based on new structural model whose state variable is specified by a dynamic business profit process. We confirmed their applicability through empirical analyses with the bankruptcy database and so on.
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| Free Research Field |
数理ファイナンス、金融工学
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