Progress in new methods for prediction theory and Tauberian theorems with applications to stochastic analysis of processes with memory

预测理论和陶伯定理新方法及其在记忆过程随机分析中的应用进展

• 批准号: 16340030
• 负责人: INOUE Akihiko
• 金额: $ 8.7万
• 依托单位: HOKKAIDO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340030/
• 关键词: 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

(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.

（1）Inoue和中野在一个具有记忆的金融市场模型中解决了两个长期投资问题。它们是期望增长率最大化和大偏差概率最大化。他们还研究了参数估计。（2）Inoue和中野推广了（1）的结果。结果表明波动率的期限结构是单调递增的。这样做的关键是解决Riccati型方程。（3）Inoue，Kasahara和Pourahmadi得到了有限数据缺失时预测的新结果。（4）Inoue，Kasahara和Pourahmadi在预测理论中引入了有限维对偶，并研究了它的性质。利用对偶性，他们统一了Kolmogorov，Yaglom和Nakazi的结果，并推广了它们。（5）井上、笠原和宾厄姆在OPUC和相关结果的基础上给出了长记忆的新定义。这个定义比基于协方差可积性的定义给出了更广泛的一类长记忆过程。FARIMA就是一个典型的例子。基于这个新定义，他们获得了FAIMA的新结果。（6）Inoue和Anh证明了离散时间有限预测的一个类似的表示定理。利用它，他们还证明了一个类似的巴克斯特不等式。（7）Inoue、Fukuda和中野发展了一种新的无差别定价理论，并利用它得到了金融保险产品定价的新结果。特别是，当效用函数是指数型时，他们得到了新的结果。

项目成果

Linear filtering of systems with memory and application to finance

带内存的系统线性过滤和金融应用

• 发表时间: 2006
• 期刊: J. Appl. Math. Stoch. Anal. Art. ID53104
• 作者: Inoue;A.;Nakano;Y.;Anh;V.
• 通讯作者: V.

Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing

具有负差分度的分数 ARIMA 过程的偏自相关函数

• 发表时间: 2004
• 期刊: Journal of Multivariate Analysis 89
• 作者: Hosokawa;Takuya;Kei Ji Izuchi;Akihiko Inoue
• 通讯作者: Akihiko Inoue

Factorization of functions in H^P(T^n)

H^P(T^n) 中函数的因式分解

• 发表时间: 2004
• 期刊: Complex Variables Th.and Appl. 49
• 作者: Izuchi;Keiji;K.Izuchi;T.Nakazi
• 通讯作者: T.Nakazi

Backward shift invariant subspaces in the bidisc. III

bidisc 中的后移不变子空间。

• 发表时间: 2004
• 期刊: Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum 70
• 作者: Hosokawa;Takuya;Kei Ji Izuchi;Akihiko Inoue;Kei Ji Izuchi;Kei Ji Izuchi;KeiJi Izuchi;Keiji Izuchi
• 通讯作者: Keiji Izuchi

Financial Markets with Memory I: Dynamic Models

• DOI: 10.1081/sap-200050096
• 发表时间: 2005-01
• 期刊: Stochastic Analysis and Applications
• 影响因子: 1.3
• 作者: Vo Anh;A. Inoue