| Project/Area Number |
19540144
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Keio University |
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Principal Investigator |
ARAI Takuji Keio University, 経済学部, 准教授 (20349830)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 確率論 / 関数解析学 / 応用数学 / ファイナンス論 / 数理ファイナンス / 価格付け理論 / 非完備市場 / リスク測度 / 効用関数 / 同値martingale測度 / Orlicz space / semimartingale |
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| Research Abstract |
I have completed my research on shortfall risk measures which appear in research on good deal bounds. Shortfall risk measures are convex risk measures representing the least price which enables a seller selling a claim to suppress her shortfall risk less than her limitation by selecting a suitable hedging strategy. Shortfall risk measures would decide candidates of prices of contingent claims.
In the first half of FY 2010, I extended results which I had obtained in FY 2009 to the case where the underlying asset price process is non-locally bounded, and succeeded in getting some results on models under cone and convex constraints. Moreover, in the second half, I studied inf-convolutions, and applied it to the shortfall risk measure problem. As a result, while I had obtained results only on Orlicz hearts which are parts of Orlicz spaces, I succeeded in extending to general Orlicz spaces.
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