| Project/Area Number |
22540149
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Keio University |
|---|
Principal Investigator |
ARAI Takuji 慶應義塾大学, 経済学部, 教授 (20349830)
|
|---|
| Project Period (FY) |
2010-04-01 – 2013-03-31
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
|---|
| 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 / 効用関数 / 同値martingale測度 / Orlicz space / Scmimartingale |
|---|
| 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.
|
