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

基本信息

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

项目摘要

(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Nakano解决了具有记忆的金融市场模型中的两个长期投资问题。它们是期望增长率的最大化和大偏差概率的最大化。他们还研究了参数估计。(2)Inoue和Nakano扩展了(1)的结果。结果承认波动性期限结构单调递增。这样做的关键是求解 Riccati 型方程。(3)Inoue、Kasahara 和 Pourahmadi 获得了关于有限数量数据丢失时的预测的新结果。(4)Inoue、Kasahara 和 Pourahmadi 在预测中引入了有限维对偶性理论并研究其性质。他们利用对偶性统一了Kolmogorov、Yaglom和Nakazi的结果，并对其进行了扩展。(5)Inoue、Kasahara和Bingham在OPUC的基础上给出了长记忆的新定义以及相关结果。与基于协方差可积性的定义相比，该定义给出了更广泛的长记忆过程类别。 FARIMA 就是一个典型的例子。他们基于这个新定义得到了FAIMA的新结果。(6)Inoue和Anh证明了离散时间有限预测中表示定理的类比。对于具有平稳增量的连续时间、长记忆模型。利用它，他们还证明了巴克斯特不等式的类比。(7)井上、福田和中野发展了一种新的无差异定价理论，并利用它获得了金融和保险产品定价的新结果。特别是，当效用函数是指数型时，他们获得了新的结果。