2012 Fiscal Year Final Research Report
The Research on precise estimate for the regularity of diffusion Operator of diffusion process with absorbed boundary condition and Its application
| Project/Area Number |
22540174
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
KUSUOKA Shigeo 東京大学, 大学院・数理科学研究科, 教授 (00114463)
|
|---|
| Project Period (FY) |
2010 – 2012
|
| Keywords | 確率解析 関数解析 |
|---|
| Research Abstract |
We studied the property and numerical computation methods for solutions of diffusion equation related to diffusion processes with absorbed boundary (Dirichlet boundary) which appears in pricing knock-out derivatives. First, we studied about precise estimates of smoothness for diffusion operators with Dirichlet boundary condition, and obtained similar estimates to estimates in the case of diffusion operators without boundary conditions. Then we studied numerical computation methods for the expectation of diffusion process with an absorbed boundary. We studied a similar method to KLNV method in the case of no boundary conditions, and obtained 3rdorder approximation formula. Unfortunately Whitakker function appears in the formula,the implementation is difficult, and so we could not do the computer simulation.
|
