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

(1)Inoue和Nakano在一个有记忆的金融市场模型中解决了两个长期投资问题。它们分别是预期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推广了(1)的结果。结果表明波动率期限结构单调递增。这样做的关键是解利卡蒂型方程。(3)Inoue、Kasahara和Pourahmadi在有限数据缺失情况下的预测得到了新的结果。(4)Inoue、Kasahara和Pourahmadi在预测理论中引入了有限维对偶，并研究了其性质。利用对偶性，他们统一了Kolmogorov， Yaglom和Nakazi的结果，并对其进行了推广。(5)Inoue、Kasahara和Bingham基于OPUC给出了长记忆的新定义和相关结果。这个定义给出了比基于协方差可积性的长记忆过程更广泛的一类。FARIMA就是一个典型的例子。基于这一新定义，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中表示定理的一个类比。对于连续时间，采用平稳增量的长记忆模型。利用它，他们还证明了巴克斯特不等式的一个类似物。(7)Inoue、Fukuda和Nakano提出了新的无差别定价理论，并利用该理论对金融保险产品的定价获得了新的结果。特别是当效用函数为指数型时，他们得到了新的结果。

(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.