基于动态数据驱动的改进灰色马尔科夫模型黄金价格预测

将黄金数据的尖峰厚尾、异方差性及杠杆效应等统计特征与马尔科夫概率转移矩阵所具有的动态变化规律结合,提出一种改进的灰色马尔科夫模型.模型首先对数据进行统计分析,建立相应的概率统计模型并用此模型对系统发展变化趋势进行拟合.在拟合序列的基础上利用马尔科夫链的动态转移变化建立状态转移概率矩阵,采用动态数据驱动原理对未来每一步数据进行动态预测.模型既是统计方法与数据动态驱动的结合,克服了传统的灰色马尔科夫模型中对数据内在统计规律的忽视,实证表明其预测精度较灰色马尔科夫模型预测高,具有较好的实用性.     

中国证券市场知情交易概率的动态马尔科夫状态转移模型研究

对指令驱动市场知情交易的研究是近年来的热点问题。常用的EKOP模型存在一些缺陷,本文放宽了EKOP模型关于日内信息均匀释放以及交易者行为独立性的假设,用动态的马尔科夫状态转移模型对该模型进行了改进,并检验了改进后的知情交易概率模型在中国证券市场的适用性。通过模拟数据以及对中国证券市场交易数据的实证研究发现动态的马尔科夫状态转移模型克服了EKOP模型受买卖方数据影响而产生的系统偏误,估计的知情交易概率更符合事后检验。     

北京市交通运输、仓储和邮政业增加值的灰色马尔科夫预测模型

将2000-2017年北京市交通运输、仓储和邮政业产值作为原始数据系列,应用灰色模型对时序数据的总体趋势进行拟合,选取相对误差作为随机波动过程,对预测结果进行修正,最后运用灰色马尔科夫模型对未来5年北京市交通运输、仓储和邮政业的产值进行实例预测.结果表明:经过马尔科夫过程修正的灰色预测模型平均预测精度由原来的90.82%提升到97.14%,预测效果明显,说明了方法对北京市交通运输、仓储和邮政业增加值预测的有效性.     

基于动态无偏灰色马尔科夫模型的煤炭需求量预测

煤炭消费系统是一个复杂的非线性系统,具有随机性、非线性、动态性等特点,科学地预测煤炭消费量及其结构对于优化配置能源有重要意义.传统的单一预测方法预测精度较低.在对陕西省煤炭消费历史数据分析的基础上,构建了煤炭消费总量的GM(1,1)模型、灰色GM(1,1)预测模型和动态无偏的马尔科夫结构预测模型.拟合结果表明,动态无偏灰色马尔科夫模型既能消除传统灰色GM(1,1)模型的固有偏差,又能提高预测精度,其平均相对误差为2.10%,分别低于传统灰色GM(1,1)模型和一般灰色马尔科夫模型的17.37%和6.37%,可用于煤炭需求的预测,在此基础上对陕西省2017-2025年煤炭消费进行了预测,为未来能源消费发展规划提供依据.     

应用RJMCMC方法识别线性模型异常点

传统线性模型异常点识别方法容易发生误判:正常点被归为异常点或者异常点被归为正常点.为解决此类问题,提出了应用逆跳马尔科夫蒙特卡洛方法识别异常点的思想,同时将其应用于实际数据加以检验,识别效果明显好于传统方法.     

基于HMM的CpG岛位置判别

隐马尔科夫过程是20世纪70年代提出来的一种统计方法,以前主要用于语音识别,1989年Churchill将其引入计算生物学,目前HMM是生物信息学中应用比较广泛的统计方法。本文对马尔科夫过程和HMM进行了简明扼要的描述,并对其在CpG岛位置判别中的应用做了概括介绍。     

我国长期护理保险设计创新及定价研究

随着我国人口老龄化程度不断加深,针对老年人的长期护理保险的定价方法成为保险精算方向的热点问题.本文利用中国老年健康影响因素跟踪调查(CLHLS) 2014–2018年的数据,在传统的三、四状态马尔科夫模型的基础上,进一步将老年人的健康状况划分为六种状态,采用马尔科夫模型对各状态进行数值测算,利用Robinson幂函数综合考虑了性别和年龄两种因素求解健康状态的转移强度矩阵和转移概率矩阵,随后运用双随机Lee-Carter模型、随机游走模型和预期寿命公式估算了65、75和85岁的保费年限,以此为依据给出了长期护理保险的保费计算方法,为我国的长期护理保险定价提供理论参考.     

基于灰色马尔科夫模型的平顶山市空气污染物浓度预测

选用平顶山市2005—2009年各空气污染物浓度作为原始数据序列,建立灰色马尔科夫预测模型,对未来10年的污染因子浓度进行预测.模型检验结果表明:均方差比值和小误差概率均为一级;运用灰色关联分析法计算各污染物原始数据序列与预测数据序列之间的关联度,定量描述灰色马尔科夫预测模型对于空气质量预测的精确度,平均精度达到99.9%,表明灰色马尔科夫预测模型对于空气质量预测有很高的实用性.     

基于灰色马尔科夫链预测模型的广西边境小额贸易预测研究——灰色系统理论应用系列论文之三

在分析广西边境小额贸易现状的基础上,运用灰色模型和马尔科夫链的基本理论,构建灰色马尔科夫模型进行了预测.结果表明,经过二阶弱化处理、灰色建模、灰色新陈代谢以及灰色马尔科夫预测的结果,能明显地提高预测精度.最后,提出了加大基础设施建设、转变边贸流通模式、构建沿边型产业开放体系、提高边境贸易便利化水平和培育发展边境特色经济带等对策建议.     

二阶离散隐马尔科夫模型的严格定义及等价性质

隐马氏模型作为一种具有双重随机过程的统计模型,具有可靠的概率统计理论基础和强有力的数学结构,已被广泛应用于语音识别、生物序列分析、金融数据分析等领域.由于传统的一阶隐马氏模型无法表示更远状态距离间的依赖关系,就可能会忽略很多有用的统计特征,故有人提出二阶隐马氏模型的概念,但此概念并不严格.本文给出二阶离散隐马尔科夫模型的严格定义,并研究了二阶离散隐马尔科夫模型的两个等价性质.     

带固定比例交易费率的跳扩散欧式期权的定价

考虑市场存在交易费率的跳扩散欧式期权的定价问题.由于交易费的存在使得传统的对冲方法不适用,我们将该问题转化为两元的随机控制问题.证明了带固定比例交易费率的跳扩散欧式期权的价格是对应的积分微分不等方程的约束粘性解,并通过马尔科夫链对变分问题进行离散,证明了在粘性意义下离散方法的收敛性.最后给出了数值结果.     

Nonlinear reserving in life insurance: Aggregation and mean-field approximation

We suggest a unified approach to claims reserving for life insurance policies with reserve-dependent payments driven by multi-state Markov chains. The associated prospective reserve is formulated as a recursive utility function using the framework of backward stochastic differential equations (BSDE). We show that the prospective reserve satisfies a nonlinear Thiele equation for Markovian BSDEs when the driver is a deterministic function of the reserve and the underlying Markov chain. Aggregation of prospective reserves for large and homogeneous insurance portfolios is considered through mean-field approximations. We show that the corresponding prospective reserve satisfies a BSDE of mean-field type and derive the associated nonlinear Thiele equation.     

A Continuous Time Financial Market with a Poisson Process as Transaction Timer

We study the influence of transactions on investors' portfolio values under the assumption that the investors' transaction times are determined by Poisson point processes, whose intensity measures can naturally be interpreted as transaction frequencies. We give lower and upper bounds on the expectations of portfolio values in terms of transaction intensities, and prove that there exist a sequence of portfolio fractions and a transaction frequency which maximize the expectation of the portfolio value for a finite horizon. We also give bounds on transaction frequencies for preventing the investors from losing money. Then the optimal transaction strategies for finite and infinite time horizons and the asymptotic effects of making transactions are discussed based on the concept of a benefit function of transactions. Finally, we investigate the influence of transactions on financial markets, with the market mean rates of return and volatilities being connected with the transaction frequency. We show that the market becomes unprofitable in a finite time if an overwhelming amount of transactions is involved and the market is suitable for some limited transactions when its trade capacity does not increase beyond any limit at a relatively high speed. Our models and simulations illustrate how the investors' collective action affects the financial market.     

Dynamic asset allocation for varied financial markets under regime switching framework

Asset allocation among diverse financial markets is essential for investors especially under situations such as the financial crisis of 2008. Portfolio optimization is the most developed method to examine the optimal decision for asset allocation. We employ the hidden Markov model to identify regimes in varied financial markets; a regime switching model gives multiple distributions and this information can convert the static mean–variance model into an optimization problem under uncertainty, which is the case for unobservable market regimes. We construct a stochastic program to optimize portfolios under the regime switching framework and use scenario generation to mathematically formulate the optimization problem. In addition, we build a simple example for a pension fund and examine the behavior of the optimal solution over time by using a rolling-horizon simulation. We conclude that the regime information helps portfolios avoid risk during left-tail events.     

Switching diffusion logistic models involving singularly perturbed Markov chains: Weak convergence and stochastic permanence

Focusing on stochastic dynamics involve continuous states as well as discrete events, this article investigates stochastic logistic model with regime switching modulated by a singular Markov chain involving a small parameter. This Markov chain undergoes weak and strong interactions, where the small parameter is used to reflect rapid rate of regime switching among each state class. Two-time-scale formulation is used to reduce the complexity. We obtain weak convergence of the underlying system so that the limit has much simpler structure. Then we utilize the structure of limit system as a bridge, to invest stochastic permanence of original system driving by a singular Markov chain with a large number of states. Sufficient conditions for stochastic permanence are obtained. A couple of examples and numerical simulations are given to illustrate our results.     

基于灰色马尔可夫模型的物流配送需求量预测研究

研究可以较准确地预测物流配送需求量的数学模型,以服务于政府及企业的物流规划及其决策.将灰色理论和离散状态的马尔可夫链相结合,用灰色马尔可夫链对物流配送需求量进行实证研究.针对灰色数据系列首先用GM模型进行趋势预测,然后利用马尔可夫状态转移概率矩阵预报方法对其预测值进行二次拟合,预测精度明显高于GM模型预测.     

A Markov Embedding Approximation for a Stochastic Population Model with Exogenous Disturbances

We present and study an approximation scheme for the mean of a stochastic simulation that models a population subject to nonlinear birth and exogenous disturbances. We use the information from the probability distribution for the disturbance times to construct a method that improves upon the mean-field approximation. We show through two example systems the effectiveness of the Markov embedding approximation and discuss the contexts in which it is an appropriate method.     

Bayesian and non-bayesian analysis of gamma stochastic frontier models by Markov Chain Monte Carlo methods

Summary  This paper considers simulation-based approaches for the gamma stochastic frontier model. Efficient Markov chain Monte Carlo methods are proposed for sampling the posterior distribution of the parameters. Maximum likelihood estimation is also discussed based on the stochastic approximation algorithm. The methods are applied to a data set of the U.S. electric utility industry. The authors are grateful to two anonymous referees for their useful comments, which improved an earlier version of the paper. The first author also thanks the financial support by the Japanese Ministry of Education, Culture, Sports, Science and Technology under the Grant-in-Aid for Scientific Research No.14730022.