2013 Fiscal Year Final Research Report
Research on pricing theory by convex risk measures taking account of hedging, and its related stochastic analysis
| Project/Area Number |
22540149
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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 慶應義塾大学, 経済学部, 教授 (20349830)
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| Project Period (FY) |
2010-04-01 – 2013-03-31
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| Keywords | 数理ファイナンス / 価格付け理論 / 非完備市場 / リスク測度 / Orlicz空間 / Good deal bound |
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| Research Abstract |
I have studied convex risk measures on stochastic processes in order to deal with shortfall risk measures for American options. In particular, I introduced spaces of stochastic processes whose maximum belongs to an Orlicz space; and obtained representation results for convex risk measures defined on such spaces. Next, I have researched on relationship between convex risk measures and good deal bounds. Supposing the market is a convex cone, I investigated (1) properties of superhedging cost, (2) the equivalence for a convex risk measure between that it represent upper and lower bounds of a good deal bound and that it is given as a risk indifference price, (3) extensions of the fundamental theorem of asset pricing. In addition, I extended the above results to the case where the market is merely convex.
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