保费调整模型的研究

在分析保险累积损失和有效投资的基础上 ,利用倒向随机微分微分方程 ,建立了以投资收益相支持的保险价格调整模型 ,并对两种常见类型的保险进行了保险价格调整分析 .对保险人通过投资改变其保险市场竞争地位有积极的作用 .最后 ,用释例进行了说明 .     

Forecasting high‐frequency financial data with the ARFIMA–ARCH model

Financial data series are often described as exhibiting two non‐standard time series features. First, variance often changes over time, with alternating phases of high and low volatility. Such behaviour is well captured by ARCH models. Second, long memory may cause a slower decay of the autocorrelation function than would be implied by ARMA models. Fractionally integrated models have been offered as explanations. Recently, the ARFIMA–ARCH model class has been suggested as a way of coping with both phenomena simultaneously. For estimation we implement the bias correction of Cox and Reid ( 1987 ). For daily data on the Swiss 1‐month Euromarket interest rate during the period 1986–1989, the ARFIMA–ARCH (5,d,2/4) model with non‐integer d is selected by AIC. Model‐based out‐of‐sample forecasts for the mean are better than predictions based on conditionally homoscedastic white noise only for longer horizons (τ > 40). Regarding volatility forecasts, however, the selected ARFIMA–ARCH models dominate. Copyright © 2001 John Wiley & Sons, Ltd.     

罗尔中值定理的推广

对罗尔中值定理进行了推广,给出了它在区间为有限开区间、无穷区间及函数为无界函数形式下结论的格式.     

极值定理的新体系

本文给出函数极值教学的一个新体系 ,强调直观性与系统性     

有关平均值的不等式及其证明

对两个平均值不等式，给出只用一元函数一阶导数的证明方法，同时对更为一般的平均值不等式，给出了统一的证明。     

直线磨擦驱动带式输送机辅机长度和位置确定的研究

在对直线摩擦驱动带式输送机生产原理、现状及典型工况分析的基础上，摸拟出10多个数学模型，并根据模型利用计算机处理计算出该类输送机正常运转时辅机长度及位置的重要参数，为优化设计提供依据。     

基于分数次Logistic方程的技术创新传播模式的稳定性分析

利用分数次微分方程的定性理论,给出了基于分数次Logistic方程网络式技术创新传播模式平衡点的稳定性分析,为创新技术的开发与积累提供了理论依据.     

多元对称函数驻点的讨论

运用严密的逻辑推理，对标准多元对称函数及非标准多元对称函数求驻点的解法做了深入的探讨，并给出了一种简洁且实用的方法。     

ARFIMA approximation and forecasting of the limiting aggregate structure of long‐memory process

This article studies Man and Tiao's (2006) low‐order autoregressive fractionally integrated moving‐average (ARFIMA) approximation to Tsai and Chan's (2005b) limiting aggregate structure of the long‐memory process. In matching the autocorrelations, we demonstrate that the approximation works well, especially for larger d values. In computing autocorrelations over long lags for larger d value, using the exact formula one might encounter numerical problems. The use of the ARFIMA(0, d, d?₁) model provides a useful alternative to compute the autocorrelations as a really close approximation. In forecasting future aggregates, we demonstrate the close performance of using the ARFIMA(0, d, d?₁) model and the exact aggregate structure. In practice, this provides a justification for the use of a low‐order ARFIMA model in predicting future aggregates of long‐memory process. Copyright © 2008 John Wiley & Sons, Ltd.     

Malliavin分析在下方约束最优投资组合中的应用

对下方约束的最优投资模型进行推广.考虑市场参数为关于时间函数的情形下,利用Malliavin分析,刻画其带下方约束的最优投资策略.