| Project/Area Number |
16340030
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | HOKKAIDO UNIVERSITY |
|---|
Principal Investigator |
INOUE Akihiko Hokkaido Univ., Fac.of Sci., Asso.Prof., 大学院理学研究院, 助教授 (50168431)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
NAKAZI Takahiko Hokkaido Univ., Fac.of Sci., Prof., 大学院理学研究院, 教授 (30002174)
KASAHARA Yukio Hokkaido Univ., Fac.of Sci., Researcher, 大学院理学研究院, 学術研究員 (10399793)
三上 敏夫 北海道大学, 大学院・理学研究科, 助教授 (70229657)
|
|---|
| Project Period (FY) |
2004 – 2006
|
| Project Status |
Completed (Fiscal Year 2006)
|
| Budget Amount *help |
¥13,600,000 (Direct Cost: ¥13,600,000)
Fiscal Year 2006: ¥5,600,000 (Direct Cost: ¥5,600,000)
Fiscal Year 2005: ¥5,600,000 (Direct Cost: ¥5,600,000)
Fiscal Year 2004: ¥2,400,000 (Direct Cost: ¥2,400,000)
|
|---|
| Keywords | Prediction theory / Orthogonal polynomials / Verblunsky coefficients / Long memory / Financial market model with memory / Long term investment / Partial autocorrelation function / Duality in prediction theory / 効用等値価格 / 記憶を持つ確立過程 / 予測問題 / 確率解析 / 記憶を持つ確率過程 / 最適投資問題 / フィルタリング / 非マルコフ型ノイズ |
|---|
| Research Abstract |
(1)Inoue and Nakano solved two long term investment problems in a financial market model with memory. They are maximization of expected growth rate and that of large deviation probability. They also studied the parameter estimation.
(2)Inoue and Nakano extended the results of (1). The result admits monotone increasing term structure of volatility. In so doing, the key is to solve Riccati-type equations.
(3)Inoue, Kasahara and Pourahmadi obtained new results concerning prediction when finite number of data are missing.
(4)Inoue, Kasahara and Pourahmadi introduced a finite dimensional duality in prediction theory and studied its properties. Using the duality, they unified the results of Kolmogorov, Yaglom and Nakazi, and also extended them.
(5)Inoue, Kasahara and Bingham gave a new definition of long memory based on OPUC and also related results. This definition gives a wider class of long memory processes than thosed based on the integrability of covariance. FARIMA is a typical example. They obtained new results for FAIMA based on this new definition.
(6)Inoue and Anh proved an analogue of representation theorems in finite prediction in discrete time.for continuous time, long memory model with stationary increments. Using it, they also proved an analogue of Baxter's inequality.
(7)Inoue, Fukuda and Nakano developed a new theory of indifference pricing and, using it, obtained new results on pricing of financial and insurance products. In particular, they obtained new results when the utility function is of exponential type.
|
