状态转移框架下跨地区、跨行业资产配置模型及实证

利用Markov状态转移模型捕捉金融资产收益率序列的非线性、动态的结构性变化,考虑不同市场状态下资金在地区板块、行业板块间流动导致的板块轮动效应,构建基于状态转移的跨地区、跨行业资产配置模型。在此基础上,对市场状态和地区、行业板块轮动效应对资产配置的影响进行细致分析。研究发现:中国股票市场存在明显的动态结构性变化,可以分为熊市状态和牛市状态,两种市场状态下最优资产配置结构不同。结果表明,状态转移框架下的跨地区和跨行业资产配置能够刻画非对称市场状态下资产的收益和风险特征,分散非系统性风险的同时降低市场风险,提高投资者的收益,可以为投资者决策提供有价值的参考。     

基于VECM-MGARCH模型的人民币汇率与牛熊股市关系研究

2005年以来人民币汇率均处于升值过程,而股市却经历了牛、熊市的历程.本文基于VECM-MGARCH模型实证研究了人民币汇率与我国股市处于牛、熊市期间二者之间的动态关系,结果发现,汇率和股价之间不存在线性的相互影响关系.就波动性而言,股市处于牛市期间,二者之间存在相互影响关系;熊市期间,这种非线性关系消失.人民币升值预期的减弱及股市的下跌是导致二者关系变化的主要原因.     

股灾背景下中美股市风险溢出的结构转换研究

选取中美股票市场的上证综指、恒生指数和标普500指数作为研究对象进行风险溢出效应研究,结果表明,总体而言上海市场与香港市场之间双向风险溢出效应最为显著,香港市场和美国市场次之,而上海市场与美国市场之间的双向风险溢出效应最不显著;从风险溢出方向与强度方面分析,无论牛熊市,香港市场对上海市场在极端风险时刻的风险溢出要显著强于上海市场对香港市场的溢出,而香港市场与美国市场之间在牛市行情下双向风险溢出效应相对均衡,在熊市行情下香港对美国的风险溢出相对更大,与常理不一致的结果是上海市场在牛市期间对香港市场的风险溢出效应要大于熊市,围绕这一点进一步采用Chi-plot相关图进行分析表明中国市场还未达到“中国打喷嚏,世界经济感冒”的状态;从风险溢出效应的动态趋势分析看出两个牛市阶段各市场的风险溢出呈现不同特征。美国市场对中国市场的风险溢出效应总体平稳,而中国市场对美国市场的风险溢出效应存在一定差异,在低分位数水平相差较大,随分位数水平提高两个牛市阶段的风险溢出趋于一致。但上海市场对香港市场的风险溢出随时间变化在牛市阶段逐步增强,而香港市场对上海市场的风险溢出则逐渐下降。     

中国股市大公司股票与小公司股票收益关系的实证研究

对中国股市的大公司股票与小公司股票的价格与收益关系进行了实证研究,结果表明大公司股票与小公司股票的收益无论在牛市阶段还是熊市阶段都存在较高的相关性;熊市阶段大公司股票收益的自相关程度最高,存在一定趋势性.大公司股票与小公司股票的价格序列是单位根的,但不是协整的,二者的收益序列是稳定的,在牛市阶段和熊市阶段大公司股票与小公司股票收益之间存在双向的领先—滞后后关系.     

Modeling dependence structure among European markets and among Asian-Pacific markets: a regime switching regular vine copula approach

This paper investigates the structure of dependence among twelve European markets and among twelve Asian-Pacific markets. The dynamic of the dependence structure is described by a two-state regime switching model. The dependence structure during a bull phase is modelled by the Gaussian copula, while dependence during a bear phase is modelled by the regular vine copula. We analyze the regular vine structure in the second regime precisely. We perform a simplification procedure using a likelihood-ratio test and discuss the substitution of general regular vines by canonical vines or drawable vines. The analysis confirms the two-state nature of financial markets in addition to asymmetric and heavy-tailed dependences. Additionally, the European market has proven to be more strongly connected than the Asian-Pacific market, and European dependences are deeper in terms of conditional dependences. The results can be used by international investors by taking into account differences of both analyzed regions. Additionally, the analysis may help with the crisis prediction. The shift time to the market phase describing crisis times occurs significantly before the crisis itself.     

中国股市大公司与小公司股票动态价格关系研究——以钢铁行业为例

从中国上海和深圳股票市场选择了钢铁股票22家,根据差别信息集理论,探究了该行业内股票价格的长期协动关系以及收益的领先—滞后关系,发现钢铁大公司股票与其小公司股票价格的长期协动关系仅存在于牛市阶段.在熊市阶段,大公司股票的收益对小公司股票收益存在信息领先趋势.并给出了实际操作建议.     

投资者过度反应与牛熊市波动非对称性

论文针对沪深股市牛熊市中所呈现出的波动非对称性的差异,从牛熊市中投资者对信息反应的差异角度予以解释。论文以非预期交易量变化率作为投资者对信息冲击反应的代理变量,研究显示投资者在牛市行情中的过度反应,是造成沪深股市牛市行情波动正向非对称性的重要原因。与此同时论文通过对比美国、香港和沪深股市上牛熊市波动非对称性差异,进一步验证沪深市场上不完善的市场机制加剧了投资者在牛市行情中的过度反应,进而导致牛市行情中的波动正向非对称性。     

整体视角下的投资者过度自信实证研究

过度自信是行为金融学中的一个重要假说。本文以证券市场整体为研究对象,采用可行的广义最小二乘法(FGLS)估计线性回归模型并结合格兰杰因果检验、指数自回归条件异方差模型(EGARCH)等对中国证券投资者过度自信情况进行实证研究。结果显示,中国投资者普遍存在着过度自信,且这种心理偏差对其投资行为产生了明显影响;与美国等成熟证券市场不同,中国投资者过度自信程度在牛市和熊市中并没有统计上的显著差别。     

When the “Bull” Meets the “Bear”—A First Passage Time Problem for a Hidden Markov Process

Let _t be a continuous Markov chain on N states. Consider adjoining a Brownian motion with this Markov chain so that the drift and the variance take different values when _t is in different states. This new process Z_t is a hidden Markov process. We study the probability distribution of the first passage time for Z_t.Our result, when applied to the stock market, provides an explicit mathematical interpretation of the fact that in finite time, there is positive probability for the bull (bear) market to become bear (bull).     

Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns

This paper studies the optimization problem of DC pension plan under mean–variance criterion. The financial market consists of cash, bond and stock. Similar to Guan and Liang (2014), we assume that the instantaneous interest rate is an affine process including the Cox–Ingersoll–Ross (CIR) model and Vasicek model. However, we assume that the expected return of the stock follows a completely different mean-reverting process, which can well display the bear and bull features of the market, and the market price of the stock index is the Ornstein–Uhlenbeck process. The pension manager thus has to undertake the risks of interest rate and market price of stock index. Besides, a special stochastic contribution rate is formulated. The goal of the pension manager is to maximize the expected terminal value and minimize the variance of terminal value. We will use the technique developed by Guan and Liang (2014) to tackle this problem and derive the closed-forms of efficient frontier and strategies. Numerical analysis is given in the end of this paper to show the economic behavior of the efficient frontier and strategies.     

Robust chaos in a credit cycle model defined by a one-dimensional piecewise smooth map

We consider a family of one-dimensional continuous piecewise smooth maps with monotone increasing and monotone decreasing branches. It is associated with a credit cycle model introduced by Matsuyama, under the assumption of the Cobb-Douglas production function. We offer a detailed analysis of the dynamics of this family. In particular, using the skew tent map as a border collision normal form we obtain the conditions of abrupt transition from an attracting fixed point to an attracting cycle or a chaotic attractor (cyclic chaotic intervals). These conditions allow us to describe the bifurcation structure of the parameter space of the map in a neighborhood of the boundary related to the border collision bifurcation of the fixed point. Particular attention is devoted to codimension-two bifurcation points. Moreover, the described bifurcation structure confirms that the chaotic attractors of the considered map are robust, that is, persistent under parameter perturbations.     

Flip bifurcations of an SIR epidemic model with birth pulse and pulse vaccination

In this paper, we study an SIR epidemic model with birth pulse and pulse vaccination. We present a new constructor method of Poincaré maps. Using this method, we construct a Poincaré map. However, for this Poincaré map, we can’t directly use the bifurcation theorem to discuss the existence of flip bifurcations. We use a new method to investigate the existence of flip bifurcations. We establish that the system undergoes flip bifurcation when the maximum birth rate passes some critical values. Furthermore, some numerical simulations are given to illustrate our results.     

基于状态转移模型的条件期望与方差——从2状态到N状态的推广

基于状态转移模型计算的条件期望与方差,可以应用到金融领域,计算和度量市场在不同状态下的收益与风险.Nielson基于2状态转移模型,计算了2状态下股市的收益率的条件期望与方差.然而,实际研究中,常需要用到3状态、甚至多状态的状态转移模型.因此,基于Nielson的研究,从2状态推广到了$N$状态.基于$N$状态转移模型计算了条件期望、条件方差及无条件期望、无条件方差,该结果更具普遍性且形式更为简洁.最后,采用计算期望与方差的方法,分析中国股市收益率与波动率.实证结果表明,中国股市除存在牛市、熊市外,还存在政策市,且其具有`` 低风险,高收益"的特点.利用$N$状态转移模型计算的期望与方差可以更合理地度量金融市场在不同情况下的收益与风险.     

Stable cycles in a Cournot duopoly model of Kopel

We consider a discrete map proposed by M. Kopel that models a nonlinear Cournot duopoly consisting of a market structure between the two opposite cases of monopoly and competition. The stability of the fixed points of the discrete dynamical system is analyzed. Synchronization of two dynamics parameters of the Cournot duopoly is considered in the computation of stability boundaries formed by parts of codim-1 bifurcation curves. We discover more on the dynamics of the map by computing numerically the critical normal form coefficients of all codim-1 and codim-2 bifurcation points and computing the associated two-parameter codim-1 curves rooted in some codim-2 points. It enables us to compute the stability domains of the low-order iterates of the map. We concentrate in particular on the second, third and fourth iterates and their relation to the period doubling, 1:3 and 1:4 resonant Neimark–Sacker points.     

股票市场监管策略的一个随机模型

研究了股市在一段有可能给社会造成危害的上涨行情中，管理者监管股市的问题＋根据股市的运行规律，建立了一个随机最优化模型，讨论了参数对解的影响，并得出了一些对股市监管有意义的结论．     

Empirical Bayes stock market portfolios

We exhibit a compound sequential Bayes portfolio selection algorithm based solely on the past which not only lives off market fluctuations but follows the drift as well. In fact, this sequential portfolio performs as well (up to first order terms in the exponent) as the optimal portfolio based on advance knowledge of the n-period empirical distribution of the market. Moreover, to first order in the exponent, the capital resulting from this portfolio will be no less than the best of the available stocks. This is a result that holds for every sample sequence. Thus bull markets and bear markets can not fool the investor into over-committing or under-committing his capital to the risky alternatives available to him. The goal is accomplished by a choice of portfolio which is robust with respect to futures that may differ drastically from the past.     

Dynamics of a generalized Gause-type predator–prey model with a seasonal functional response

We extend a previous Gause-type predator–prey model to include a general monotonic and bounded seasonally varying functional response. The model exhibits rich dynamical behaviour not encountered when the functional response is not seasonally forced. A theoretical analysis is performed on the model to investigate the global stability of the boundary equilibria and the existence of periodic solutions. It is shown that, under certain well-defined conditions, the Poincaré map of the model undergoes a Hopf bifurcation leading to the appearance of a quasi-periodic solution. Numerical results are given for the Poincaré sections and bifurcation diagrams for Holling-types II and III functional responses, using the amplitude of seasonal variation as bifurcation parameter. The model shows a rich variety of behaviour, including period doubling, quasi-periodicity, chaos, transient chaos, and windows of periodicity.     

基于投资者情绪的市场均衡分析

在行为金融研究框架下,通过分析情绪投资者与理性投资者的市场均衡条件,构建基于投资者情绪的资产定价模型,并对模型进行了数值模拟。结果表明,投资者情绪是影响资产价格的重要因素:被情绪投资者高估的资产,其回报将下降;被情绪投资者低估的资产,其回报将增加;资产回报的变化程度与情绪投资者卖出低估资产的份额正相关,与资产预期回报金额的相关系数负相关;并且,乐观情绪与悲观情绪对资产价格的作用是非对称的。     

Bifurcation analysis in an SIR epidemic model with birth pulse and pulse vaccination

The dynamical behavior of an SIR epidemic model with birth pulse and pulse vaccination is discussed by means of both theoretical and numerical ways. This paper investigates the existence and stability of the infection-free periodic solution and the epidemic periodic solution. By using the impulsive effects, a Poincaré map is obtained. The Poincaré map, center manifold theorem, and bifurcation theorem are used to discuss flip bifurcation and bifurcation of the epidemic periodic solution. Moreover, the numerical results show that the epidemic periodic solution (period-one) bifurcates from the infection-free periodic solution through a supercritical bifurcation, the period-two solution bifurcates from the epidemic periodic solution through flip bifurcation, and the chaotic solution generated via a cascade of period-doubling bifurcations, which are in good agreement with the theoretical analysis.