Erlang(2)过程的风险分析与美式看跌期权

在经典的风险理论中涉及到的索赔风险是服从复合Poission过程的, 与之不同, 我们考虑Erlang(2)风险过程\bd Erlang(2)分布往往见诸于控制理论中, 这里它作为索赔发生间隔时间的分布被引入了\bd 本文中, 我们介绍一个与破产时刻、破产前时刻的盈余以及破产时刻赤字有关的辅助函数$\phi(\cdot)$, 函数中涉及的这三个变量对风险模型的研究都是最基本也是最重要的\bdWillmot and Lin (1999)曾在古典连续时间风险模型之中研讨过这一函数\bd受Gerber and Shi(1997)及Willmot and Lin (2000)在古典模型下的研究过程的启发, 本文的一个重要结果就是找到破产前时刻的盈余以及破产时刻赤字的联合分布密度函数\bd 更得益于Gerber and Landry (1998)及Gerber and Shiu (1999)的思想, 我们应用以上的结果去寻求基础资产服从一定风险资产价格过程的美式看跌期权最优交易策略.     

在风险投资下破产概率的一个渐近显式

在本文中, 我们研究了一个离散时间风险模型的破产概率\bd 在此风险模型中, 保险公司的剩余资本被用于进行风险投资\bd 我们运用纯概率的手法建立了无限时间破产概率的渐近显式, 从而将Tang和Tsitsiashvili (2003)近期的一个结果推广到了无限时间的场合.     

对部分线性模型用惩罚最小二乘估计时最优光滑化的注记

部分线性模型也就是响应变量关于一个或者多个协变量是线性的, 但对于其他的协变量是非线性的关系\bd 对于部分线性模型中的参数和非参数部分的估计方法, 惩罚最小二乘估计是重要的估计方法之一\bd 对于这种估计方法, 广义交叉验证法提供了一种确定光滑参数的方法\bd 但是, 在部分线性模型中, 用广义交叉验证法确定光滑参数的最优性还没有被证明\bd 本文证明了利用惩罚最小二乘估计对于部分线性模型估计时, 用广义交叉验证法选择光滑参数的最优性\bd 通过模拟验证了本文中所提出的用广义交叉验证法选择光滑参数具有很好的效果, 同时, 本文在模拟部分比较了广义交叉验证和最小二乘交叉验证的优劣.     

价值风险的非参数估计方法*

价值风险(VaR)模型是当今最流行的金融资产风险管理和控制的工具之一\bd 本文提出了用局部分位数回归的方法来估计某一投资组合的VaR值\bd 该方法可用于计算投资组合多持续期的VaR, 使得人们可以了解到该投资组合在一定持续期内的动态风险\bd 本文通过模拟和美国三个月到期国债利率数据的分析说明了该方法的具体执行情况, 并与J.P. Morgan的时间开方规则作了比较\bd 结果表明我们的VaR估计有令人满意的效果.     

尺度参数变点的非参数检验

本文讨论了尺度参数模型参数变点的假设检验问题\bd 基于两样本$U$\,-统计量, 我们给出了两个检验, 并且研究了检验统计量分布的极限性质\bd 我们证明了这两个检验统计量的极限分布分别是$\sup\limits_{0相似文献   

指数族非线性混合效应模型基于$Q$函数的数据删除度量

对指数族非线性混合效应模型, 本文基于$Q$函数(朱宏图, 2001)方法, 给出几种度量数据删除影响的统计量\bd 其主要思想是将随机效应视为缺失数据, 并利用EM算法来处理完全数据对数似然函数的条件期望\bd 一个实际例子说明我们方法是有效的     

关于有信用风险的期权定价的鞅方法

本文考虑了一个关于具有对方风险的衍生物的金融模型\bd 应用公司价值模型, 本文讨论了关于具有对方破产风险的衍生物的欧式期权定价问题\bd 应用鞅方法, 在高斯分布等的假设下本文得到并证明一个关于该期权的显式Black-Scholes定价公式\bd 该公式推广了Ammann在[1]中的相应结果.     

广义线性度量误差模型

在线性度量误差模型中, 需要假设所有变量的观测值都含有未知度量误差\bd 因而 该模型不适用于一部分变量的观测值含有度量误差、而另一部分变量的观测值可精 确得到的情况\bd 为此, 本文提出了广义函数、结构和超结构关系线性度量误差模 型\bd 进一步, 这里还讨论了这些广义线性度量误差模型中参数的最小二乘和极大 似然估计方法, 给出了参数估计的表达式     

混合指数分布的参数估计

混合指数分布是寿命数据分析中一个非常重要的统计模型\bd 但是利用正规的统计方法如矩估计、极大似然估计等估计模型的参数往往比较困难\bd 本文应用EM算法详细研究了混合指数分布在正常工作条件下和在进行恒加应力加速寿命实验条件下, 在完全数据场合、I-型截尾和II-型截尾场合的参数估计问题\bd 模拟说明利用EM算法来估计混合指数分布是一种非常有效的方法.     

具有均匀结构的多元$t$\,-模型的局部影响分析

本文研究具有均匀结构的多元$t$\,-模型的局部影响分析问题\bd 依据Cook的曲率度量, 我们考虑了微小扰动对统计推断的影响, 由此导出了局部影响分析中最为关心的统计量---最大曲率方向\bd作为一种应用, 本文还祥细讨论了常见的协方差加权扰动形式.     

Stochastic differential equations with time-dependent reflecting barriers

We study existence, uniqueness and stability of solutions of stochastic differential equations with time-dependent reflecting barriers in the general case where compensating reflection processes are not necessarily of bounded variations and solutions need not be semimartingales. Applications to models of stock prices with natural boundaries of Bollinger bands type are given.     

Stochastic volatility model and technical analysis of stock price

In the stock market, some popular technical analysis indicators (e.g. Bollinger Bands, RSI, ROC, ...) are widely used by traders. They use the daily (hourly, weekly, ...) stock prices as samples of certain statistics and use the observed relative frequency to show the validity of those well-known indicators. However, those samples are not independent, so the classical sample survey theory does not apply. In earlier research, we discussed the law of large numbers related to those observations when one assumes Black-Scholes’ stock price model. In this paper, we extend the above results to the more popular stochastic volatility model.     

Fractional Liu process with application to finance

As a fuzzy counterpart of Brownian motion, Liu process has attracted more and more attention in the recent literature. In this paper, the concept of fractional Liu process is proposed as an extension of Liu process. Furthermore, we obtain the expressions of the membership functions, expected values and variances of arithmetic and geometric fractional Liu processes for each fixed time. As an application, geometric fractional Liu process is assumed to characterize the stock price, which formulates a new fuzzy stock model. Based on this proposed model, European option pricing formulas are gained and two numerical examples are given with different parameters.     

Development and implementation of a real time statistical control method to identify the start and end of the winter surge in demand for paediatric intensive care

Winter surge management in intensive care is hampered by the annual variability in the winter surge. We aimed to develop a real-time monitoring system that could promptly identify the start, and accurately predict the end, of the winter surge in a paediatric intensive care (PIC) setting. We adapted a statistical process control method from the stock market called “Bollinger bands” that compares current levels of demand for PIC services to thresholds based on the medium term average demand. Algorithms to identify the start and end of the surge were developed for a specific PIC service: the North Thames Children's Acute Transport Service (CATS) using eight winters of data (2005–12) to tune the algorithms and one winter to test the final method (2013/14). The optimal Bollinger band thresholds were 1.2 and 1 standard deviations above and below a 41-day moving average of demand respectively. A simple linear model was found to predict the end of the surge and overall demand volume as soon as the start had been identified. Applying the method to the validation winter of 2013/14 showed excellent performance, with the surge identified from 18th November 2013 to 4th January 2014.An Excel tool running the algorithms has been in use within CATS since September 2014. There were three factors which facilitated the successful implementation of this tool: the perceived problem was pressing and identified by the clinical team; there was close clinical engagement throughout and substantial effort was made to develop an easy-to-use Excel tool for sustainable use.     

上海股市若干问题分析

借助数学模型探讨股票投资问题.以每日获取最大利润为目标,建立线性规划模型;以市场布林线算法为评价标准划分时期,并建立不同时期的多指标模糊综合评价模型;采用三次指数平滑方法对上证指数进行预测并验证;根据股票价格偏离价值程度图,分析上海股市存在的泡沫情况.     

基于随机波动模型的沪深股市波动分析——以06,07年度沪深股指为例

基于马尔科夫链蒙特卡罗(MCMC)模拟的贝叶斯(Bayes)分析方法,应用随机波动(SV)模型实证分析06、07年度中国股票市场指数的波动性,并对比沪市与深市的股指,对不同形式的SV模型的参数进行估计,对结论作出合理的解释.     

Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion

A simultaneous confidence band provides useful information on the plausible range of the unknown regression model, and different confidence bands can often be constructed for the same regression model. For a simple regression line, Liu and Hayter [W. Liu, A.J. Hayter, Minimum area confidence set optimality for confidence bands in simple linear regression, J. Amer. Statist. Assoc. 102 (477) (2007) pp. 181–190] proposed the use of the area of the confidence set corresponding to a confidence band as an optimality criterion in comparison of confidence bands; the smaller the area of the confidence set, the better the corresponding confidence band. This minimum area confidence set (MACS) criterion can be generalized to a minimum volume confidence set (MVCS) criterion in the study of confidence bands for a multiple linear regression model. In this paper hyperbolic and constant width confidence bands for a multiple linear regression model over a particular ellipsoidal region of the predictor variables are compared under the MVCS criterion. It is observed that whether one band is better than the other depends on the magnitude of one particular angle that determines the size of the predictor variable region. When the angle and hence the size of the predictor variable region is small, the constant width band is better than the hyperbolic band but only marginally. When the angle and hence the size of the predictor variable region is large the hyperbolic band can be substantially better than the constant width band.     

不确定微分方程的数值解法及其应用研究

不确定微分方程广泛应用于不确定财政、不确定控制、不确定微分博弈等领域。由于一些不确定微分方程解析解难以实现,本文首先研究了不确定微分方程的Euler方法和Runge-Kutta方法两种数值解法,并进行误差分析。通过比较随机领域Black-Scholes模型和不确定领域Liu模型的欧式期权定价公式,验证不确定微分方程描述证券市场的合理性和实用性。     

EMD结合RBF神经网络新混合模型及股指期货价格预测

中国近4年才成立的股指期货市场价格呈现出非平稳、非线性的信号特征,传统的预测方法无法对长相关序列进行精确预测.将EMD与RBF相结合,建立了一种新的预测方法对我国股指期货日结算价格进行预测.结果显示本模型将原本具有长相关性质的原始序列分解为若干个短相关性质的不同频带,解决了原始序列随机性强,以及因相邻频带的干扰而造成的系统动力信息反映不足的缺陷;并与其他预测模型进行比较,显示出较高的预测精度.     

Are we using the wrong letters? An analysis of executive stock option Greeks

Greek letters, in particular delta and vega based on the Black–Scholes model (BS), have been widely used to estimate the sensitivity of CEO wealth to changes in stock price (delta) and stock return volatility (vega) and to evaluate the executive stock options (ESOs) granted on the basis of performance and risk. However, the BS model does not take into account the main features of ESOs and therefore the delta and vega values it produces are not valid. The Cvitanic–Wiener–Zapatero model (CWZ) is an alternative model to Black–Scholes for valuing ESOs. It has a closed formula and considers the main features of ESOs. We carry out a sensitivity analysis to show that research on option-based compensation and its risk-taking effects is not robust in ESO pricing models. The sensitivity analysis consists of comparing the impact of the common parameters of the BS and CWZ models, as well as the effect of the specific parameters of the CWZ model, on the sensitivity of CEO wealth to stock price and stock volatility. Additionally, using panel data methodology, we develop an empirical analysis to illustrate the influence of stock return volatility and different corporate policies on both CEO wealth sensitivities.