2003 Fiscal Year Final Research Report Summary
Tauberian and Mercerian theorems and analysis of stochastic financial processes
| Project/Area Number |
14540147
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | HOKKAIDO UNIVERSITY |
|---|
Principal Investigator |
INOUE Akihiko Hokkaido Univ., Grad.School of Sci., Asso.Prof., 大学院・理学研究科, 助教授 (50168431)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MIKAMI Toshio Hokkaido Univ., Grad.School of Sci., Asso.Prof., 大学院・理学研究科, 助教授 (70229657)
ARAI Asao Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (80134807)
|
|---|
| Project Period (FY) |
2002 – 2003
|
| Keywords | Tauberian theorem / fractional Brownian motion / partial autocorrelation function / predictor coefficient / expected utility maximization / innovation process / financial market model |
|---|
| Research Abstract |
We introduced a generalized fractional Brownian motion and proved a finite-past prediction formula for it using Tauberian theorems and a new prediction-theoretic approach.
By applying a new prediction-theoretic approach to stationary time series, we proved a surprisingly simple representation theorem for the partial autocorrelation function Using the result, we derived a precise asymptotic behavior with remainder for it.
We introduced a class of stationary increments processes which are described by continuous-time AR-equations of infinite order. We also considered SDE with the stationary increments process as driving force. In this way, we introduced stock price processes with long or short memory. We discussed about completeness and behavior of volatility of the financial market with this stock price process. We obtained an explicit representation of the innovation process associated with the drinving force, using a new prediction-theoretic approach. In this way, we solved the problem of expected utility maximization problem in the financial market. In the simplest case, this is a paremetric model that has only two additional parameters compared with the Black-Scholes model. We observed that this model well describes the real market data such as S & P500. This shows the usefulness of the model.
|
