Evolutionary model of the growth and size of firms

The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat’s law of proportionate effects as the result of the competition between products. Applying a preferential attachment mechanism for firms, the theory allows to establish the size distribution of products and firms. Also established are the growth rate and price distribution of consumer goods. Taking into account the characteristic property of human activities to occur in bursts, the model allows also an explanation of the size–variance relationship of the growth rate distribution of products and firms. Further the product life cycle, the learning (experience) curve and the market size in terms of the mean number of firms that can survive in a market are derived. The model also suggests the existence of an invariant of a market as the ratio of total profit to total revenue. The relationship between a neo-classic and an evolutionary view of a market is discussed. The comparison with empirical investigations suggests that the theory is able to describe the main stylized facts concerning the size and growth of firms.     

Dynamics of bid–ask spread return and volatility of the Chinese stock market

The bid–ask spread is taken as an important measure of the financial market liquidity. In this article, we study the dynamics of the spread return and the spread volatility of four liquid stocks in the Chinese stock market, including the memory effect and the multifractal nature. By investigating the autocorrelation function and the Detrended Fluctuation Analysis (DFA), we find that the spread return is the lack of long-range memory, while the spread volatility is long-range time correlated. Besides, the spread volatilities of different stocks present long-range cross-correlations. Moreover, by applying the Multifractal Detrended Fluctuation Analysis (MF-DFA), the spread return is observed to possess a strong multifractality, which is similar to the dynamics of a variety of financial quantities. Different from the spread return, the spread volatility exhibits a weak multifractal nature.     

Testing for persistent deviations of stock prices to dividends in the Nasdaq index

In this paper we test for the presence of bubbles in the Nasdaq stock market index over the period 1994–2003 applying fractional integration techniques and allowing for structural breaks and non-linear adjustments of prices to dividends. The results show a significant structural break in 1998 for all model specifications and data periodicity. Furthermore, we do not find evidence of asymmetric adjustment of prices to dividends when using M-TAR and TAR models. The evidence of bubbles varies depending on the data periodicity and model specification used in the analysis. Finally, the results show persistent deviations of stock prices to dividends in all cases considered, though we only find evidence of bubbles in the Nasdaq index when using weekly data for the time period after June 1998.     

An intermediate distribution between Gaussian and Cauchy distributions

In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because many kinds of distributions have no moment, we introduce weighted moments. Specifically, we consider weighted moments under two types of weighted functions: the cut-off function and the exponential function. Through these two types of weighted functions, we can obtain weighted moments for almost all distributions. We consider an application of the probability density function of the intermediate distribution on the spectral line broadening in laser theory. Moreover, we utilize the intermediate distribution to the problem of the stock market return in quantitative finance.     

Optimal timing of interventions in fishery resource and pest management

Assuming that a fish population follows the continuous logistic growth or the discrete Beverton-Holt model, several optimal impulsive harvesting policies for the maximum stock level of the fish at the end of a fishing season are investigated under the condition of fixed intensity and frequency of impulsive harvesting. The optimal impulsive harvesting moments for all cases considered are given analytically and the related numerical simulations are also provided. Furthermore, the methods employed can also be used to investigate the optimal timing of chemical control in pest management. Our results confirm that the optimal timing of pesticide applications such that the density of the pest population is minimal at any time during a planting season or the average of density of the pest population over the planting season is minimal is the beginning of the planting season. In practice, the results can be used to guide the fisherman to manage fisheries and guide farmers to control pests.     

一类商业竞争策略的模型和研究

市场份额的竞争越来越被企业所重视,这一点可以从最近几年全球企业的兼并热潮中得到例证.企业的市场份额通常由企业内在结构、竞争对手的行为和市场容量这三者决定.本文以这三者为基础而建立的模型,不仅能解释对手行为和市场容量对企业竞争的影响,还能给出企业内在结构与企业最优利润和企业最优市场份额的定量关系,因此它更适合于市场经济中的企业竞争分析.此外,本文的研究对国家的税收征管也具有一定的参考价值.     

股票收盘价波动数学模型及其应用分析

本文以股票收盘价波动因素分析成熟的定性理论及证券操作经验为基础,建立股票收盘价的数学模型,并应用该模型对某种股票作了实证分析,阐述了该方法在实践中的意义。     

股票市场模型和不变价格流形

本文首次提出股票市场价格流形的概念 ,并对由维纳过程 (布朗运动 )驱动的市场价格动态扩散过程模型 (X)的不变流形作了初步的讨论 ,给出了一个判定一个给定的价格流形M是市场模型 (X)的不变流形的充分条件 .     

用自回归模型预测中国股市未来现金股利水平

对中国股市1996年以后所发放的现金股利的分布规律进行了研究,发现中国股市现金股利增量时间序列近似符合平稳过程。在此基础上探讨了利用线性模型技术的自回归(AR)模型对未来股利水平进行预测的一些技术问题,然后运用蒙特卡罗技术对现金股利增量进行了模拟试验,产生了足够多的数据并得出了拟合预报方程。最后对未来四十年中国股市现金股利的发放水平进行了预测。     

An approximation algorithm for cutting out convex polygons

We provide an O(logn)-approximation algorithm for the following problem. Given a convex n-gon P, drawn on a convex piece of paper, cut P out of the piece of paper in the cheapest possible way. No polynomial-time approximation algorithm was known for this problem posed in 1985.