The Determinants of Stock Price Volatility: An Industry Study

The currently ongoing IT-revolution is a great challenge for economists. The industry displays ever arising new technologies, unstable market shares, long-term swings, and short-term volatility of stock prices. Yet, to study those phenomena empirically one is constrained by a lack of data. The U.S. auto industry, for which long-term time series are available, has shared a similar experience since its early development. This paper studies how long-term swings and short-term stock price volatility in the U.S. auto industry is related to innovative efforts and switching of market shares of firms. The early period of the life-cycle of the industry was characterized by high product innovation, high market share instability, volatile stock prices, and the later period by fewer firms, process innovation, more stable market shares and less stock price volatility. In this paper we focus on the transition period leading from the first to the second period and study the relation of innovative effort, market share fluctuations and stock price dynamics. After presenting stylized facts on the life-cycle of the industry we introduce a dynamic model that is able to replicate some of the stylized facts. The dynamic model admits heterogeneous firms and encompasses both evolutionary as well as optimizing approaches.     

Nonlinear delay difference equations for housing dynamics assuming heterogeneous backward-looking expectations

China's first interest rate hike during the last decade, aiming to cool down the seemingly overheated real estate market, had aroused more caution on housing market. This paper aims to analyze the housing price dynamics after an unanticipated economic shock, which was believed to have similar properties with the back ward- looking expectation models. The analysis of the housing price dynamics is based on the cobweb model with a simple user cost affected demand and a stock-flow supply assumption. Several nth-order delay rational difference equations are set up to illustrate the properties of housing dynamics phenomena, such as the equilibrium or oscillations, overshoot or undershoot and convergent or divergent, for a kind of heterogeneous backward-looking expectation models. The results show that demand elasticity is less than supply elasticity is not a necessary condition for the occurrence of oscillation. The housing price dynamics will vary substantially with the heterogeneous backward-looking expectation assumption and some other endogenous factors.     

Parameter identification and synchronization of uncertain general complex networks via adaptive-impulsive control

Multifractal theory has been widely used in kinds of field. In this paper, methods were proposed to study in the power-law auto-correlation and cross-correlation of power operating data based on multifractal detrended analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DXA). We find that both the price and the load time series in California power market and PJM power market exhibit long-term correlation. And the cross-correlation behaviors of the two series in each power market and between the two markets are also analyzed by the method MF-DXA after testing the existence of the cross-correlation of the above power operating data. However, there are some differences in the cross-correlation behaviors between the two markets. It shows that the cross-correlation of the price and the load is significant in every time periods in California 1999 power market, but in the year of 2000 in the same region market, the cross-correlation is insignificant in most time periods. Meanwhile, we conclude that cross-correlation is weaker in the California market than in the PJM market by studying the two consecutive years of the California 1999–2000 and PJM 2001–2002 power markets. We also discuss how the time intervals affect the cross-correlation exponents of the power operating data based on time-delay MF-DXA. An interesting finding is that the biggest cross-correlation exponent of the two series appeared in about 12 days time delay for the PJM 2001 power market and strongest cross-correlation in the California 1999 power market is found in lots of cyclical time intervals.     

A heterogeneous boundedly rational expectation model for housing market

This research aims to test the housing price dynamics when considering heterogeneous boundedly rational expectations such as naive expectation, adaptive expectation and biased belief. The housing market is investigated as an evolutionary system with heterogeneous and competing expectations. The results show that the dynamics of the expected housing price varies substantially when heterogeneous expectations are considered together with some other endogenous factors. Simulation results explain some stylized phenomena such as equilibrium or oscillation, convergence or divergence, and over-shooting or under-shooting. Furthermore, the results suggest that variation of the proportion of groups of agents is basically dependent on the selected strategies. It also indicates that control policies should be chosen carefully in consistence with a unique real estate market during a unique period since certain parameter portfolio may increase or suppress oscillation.     

Complexity of triopoly price game in Chinese cold rolled steel market

This paper considers a Bertrand model based on nonlinear demand functions which are closer to reality and different from previous studies. We apply the model into Chinese cold rolled steel market and study game process of triopoly. By using the theory of bifurcations of dynamical systems, local stable region of Nash equilibrium point is obtained. Simulations show complex dynamical behaviors of the system. The results illustrate that altering the relevant parameters of system can affect the stability of Nash equilibrium point and cause chaos to occur, and the complex dynamical behaviors will disappear by parameters control method. The results have an important theoretical and practical significance to Chinese cold rolled steel market.     

A fractional calculus interpretation of the fractional volatility model

Based on criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, the model is formulated in terms of a fractional integration of stochastic processes.     

Chaos,border collisions and stylized empirical facts in an asset pricing model with heterogeneous agents

Nonlinear Dynamics - An asset pricing model with chartists, fundamentalists and trend followers is considered. A market maker adjusts the asset price in the direction of the excess demand at the...     

Complex system and influence of delayed decision on the stability of a triopoly price game model

A triopoly price game model has been established based on nonlinear and economics theories in this paper, and all 3 firms of triopoly market are supposed to make a price decision with bounded rationality. By discrete dynamical system theory and jury condition, we obtain the expression of Nash equilibrium point’s stable region. Then traditional two-dimensional and creative three-dimensional diagrams of the local stable region are given by numerical simulation, and both 2D and 3D diagrams showed us some law about the Nash equilibrium point’s stable region. First, the number of time-delay decision makers has no necessary relationship with system stability; Second, under the same number of time-delay decision makers, the delay parameter has a positive influence of system stability, i.e., the price making relying more on current period profits can lower the system risk of falling into chaos. These results have significant theoretical and practical value to the price making of firms in related markets.     

并行计算机和计算流体力学并行算法

对研制计算流体力学高效并行算法及软件具有重要意义的并行计算问题提出了导引性的看法．首先综述了并行计算机的主要设计特征并简要描述了市场现有的几种并行系统．接着介绍了一些有关研制并行算法及评价其性能的重要概念．然后讨论了如何使分布式内存并行计算机的运行负载不平衡和通信开销达到最小．最后列举了计算流体力学某些算例的测试结果．本文的重点是结构网格和分程序结构网格的应用，但这些概念和方法对非结构网格同样有效     

The research on price game model and its complex characteristics of triopoly in different decision-making rule

Based on a detailed analysis of the international market, we establish a decentralized dynamics model to describe the situation that a new oligarch wishes to enter into a market which has been occupied by two oligarchs, so they have different decision rules. Then we establish and analyze the corresponding continuity system, and in detail discuss the Lyapunov exponent of this system, studying the influence of the parameter’s change to the Lyapunov exponent in three situations. Proceeding to the next step, we make the analysis of the complex dynamics behavior, such as Hopf bifurcation, chaos attractor and initial sensibility. We make a numerical simulation under different conditions, and the result shows that the process of game will tend to a Nash equilibrium at a lower price adjustment speed, and with the increase of the value, the system will appear to be unstable and go into a chaos state gradually. However, for the new entrant, the influence of chaos is not huge, and the new entrant can be seen as a stable element in the chaotic market. The research leads to a good guidance to the market with a new entrant to do the best decision-making.     

Innovation Systems by Nonlinear Networks

Cellular Neural Networks (CNNs) constitute a powerful paradigm for modeling complex systems. Innovation systems are complex systems in which small and medium enterprises play the role of simple units interacting with each other. In this paper, innovation systems based on CNN are investigated. It is shown how a model based on CNN can reproduce the main features of innovation systems and how this model can be generalized to include different aspects of the actors of the financial market.     

Complexity analysis of the dual-channel supply chain model with delay decision

In the oligopoly e-commerce market, the oligarch retailers sell products through traditional channel, while others through both network and traditional channel in order to obtain greater profits. Instead of discussing classic Bertrand game model, which past studies have done, we considered dual-channel retailer who makes price decision through both in network channel and traditional channel. This paper used the bifurcation theory of dynamical system, considering dual-channel retailer who makes delay decision. We performed a numerical simulation on system with different conditions, and some complex phenomenons occured, such as bifurcation and chaos. The results showed that adopting price delay decision in tradition channel would make the system more stable. While, adopting price delay decision in network channel makes the system less stable. When the market is in chaotic state, the using of delay decision would have an effect on the system stability in either traditional or network channels. The system become stable from chaos and would return to chaotic again with the increasing of weight in past period. Some interesting phenomenons happened when dual-channel retailer adopted delay decision in both channels. The superposition of delay decision would make the system more complex. At last, we measured the system’s performance by using profit index. We analyzed the profits of different oligarchs when the system is in different states. When the system is in chaos, the total profits of the oligarchs are obviously less than that in a stable state. Adopting delay decision is a way to avoid profit loss when system is in chaotic period, but this requires the retailer has rich operational experience. That is because adopting delayed decision may not always enhance the competitive strength of oligarchs.     

Overconfident agents and evolving financial networks

In this paper, we investigate the impact of agent personality on the complex dynamics taking place in financial markets. Leveraging recent findings, we model the artificial financial market as a complex evolving network: we consider discrete dynamics for the node state variables, which are updated at each trading session, while the edge state variables, which define a network of mutual influence, evolve continuously with time. This evolution depends on the way the agents rank their trading abilities in the network. By means of extensive numerical simulations in selected scenarios, we shed light on the role of overconfident agents in shaping the emerging network topology, thus impacting on the overall market dynamics.     

A model of chaotic drug markets and their control

This paper explores the idea that drug markets may be chaotic in a mathematical sense by considering a discrete-time model of populations of drug users and drug sellers for which initiation into either population is a function of relative numbers of both populations. The structure of the system follows that considered in an arms control context by Behrens, Feichtinger and Prskawetz (Behrens D.A., Feichtinger G., & Prskawetz A. (1997). Complex Dynamics and Control of Arms Race. European Journal of Operations Research, 100, 192-215). The model presented in this paper summarizes prerequisites for possible chaotic behavior of the number of addicts and drug dealers frequenting a local drug market. Interestingly, even if the uncontrolled market dynamics do not exhibit chaotic patterns, a static intervention like removing a constant fraction of addicts each time period can easily create chaos--but even if static control would create chaos, dynamic controls can be crafted that avoid it. Especially OGY controls seem to work well for this example.     

BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅰ)——BASIC EQUATIONS

This paper studies computational stock market by using network model and similar methodology used in solid mechanics. Four simultaneous basic equations, i.e., equation of interest rate and amount of circulating fund, equations of purchasing and selling of share, equation of changing rate of share price, and equation of interest rate, share price and its changing rate, have been established. Discussions mainly on the solution and its simple applications of the equation of interst rate and amount of circulating fund are given. The discussions also involve the proof of tending to the equilibrium state of network of stock market based on the time discrete form of the equation by using Banach theorem of contraction mapping and the influence of amount of circulating fund with exponential attenuation due to the decreasing of banking interest rate.     

The application and complexity analysis about a high-dimension discrete dynamical system based on heterogeneous triopoly game with multi-product

In production practice, firms usually produce multi-products rather than single products to obtain cost-saving advantages, cater for the diversity of consumer tastes and provide a barrier to entry. Based on nonlinear and economics theories, this paper establishes a discrete triopoly dynamical model which considers multi-product firms with heterogeneous expectations: naïve, adaptive and bounded rationality expectations. The discrete model is described by a 6-dimensional dynamical system. Thesis explores the path of the complexity of evolution and its intrinsic regularity, studies the influence of parameter change on the sensitivity level. The stable conditions of Cournot Nash equilibrium point are analyzed. The route to complex dynamics is investigated using 2-D and creative 3-D bifurcation diagrams by numerical experiment. The results show: the adaptive parameters can modify the stability of the market, but cannot lead to chaos independently; the bounded rationality parameters can arouse chaos for the whole market; larger differentiated degree of multi-product can suppress instability which is caused by adaptive and bounded rationality adjustment parameters. These results have significant theoretical and practical value to multi-product triopoly game with heterogeneous expectations in related markets.     

Dynamical behavior of a competition model of Telcom and Cable Television industry

Under the trend of the integration of the Internet, Telcom, and Cable Television (CATV) in China, the penetration and integration in the service of CATV industry and telecom industry will be conducted. With its service changing from the original single video transmission to the diverse communication service, the CATV industry will transform its development plan, thus the adjustment of its developmental strategies. From the influence of the involvement of the three telecommunication operators in Internet Protocol Television (IPTV) on CATV industry and the mutual competitive relationship among them, an analysis of the operating enterprises of the two industries was made by using differential equations. The results show that, under some conditions, one operator in the telecom industry will monopolize the market. And under other conditions, market share of the three operators in IPTV will change periodically.     

Complexity analysis of a Cournot–Bertrand duopoly game with different expectations

In this paper, we consider a Cournot–Bertrand mixed duopoly model with different expectations, where the market has linear demand and the firms have fixed marginal cost functions. Two firms choose output and price as decision variables, respectively, under the assumption that there is a certain degree of differentiation between the products offered by firms to avoid the whole market is occupied by the one that applies a lower price. The two players are considered to have bounded rational and static expectations. The existence and local stability condition of Nash equilibrium is investigated. We find the stability region of Cournot–Bertrand system is bigger than that of Cournot or Bertrand system under the same conditions. Furthermore, there are two different kinds of bifurcations when the parameters pass through the different boundary curves of the stability region, which is different from the Cournot or Bertrand model. Numerical simulation method is used to display the dynamic behaviors of the dynamical system, such as periodic cycles, bifurcation diagrams and strange attractors of the systems. The economic explanations of the complex dynamic behaviors are also given.     

The research on Cournot–Bertrand duopoly model with heterogeneous goods and its complex characteristics

This paper details the research of the Cournot–Bertrand duopoly model with the application of nonlinear dynamics theory. We analyze the stability of the fixed points by numerical simulation; from the result we found that there exists only one Nash equilibrium point. To recognize the chaotic behavior of the system, we give the bifurcation diagram and Lyapunov exponent spectrum along with the corresponding chaotic attractor. Our study finds that either the change of output modification speed or the change of price modification speed will cause the market to the chaotic state which is disadvantageous for both of the firms. The introduction of chaos control strategies can bring the market back to orderly competition. We exert control on the system with the application of the state feedback method and the parameter variation control method. The conclusion has great significance in theory innovation and practice.     

Speculative Price Dynamics in a Heterogeneous Agent Model

This paper proposes an agent model of financial markets and analyzes factors leading to speculative bubbles and speculative chaos of the asset price. A financial market is thought to contain two typical types of traders: fundamentalists and chartists who try to maximize their utility. It is shown that the nonlinearity of the excess demand functions, which are derived as a result of the traders' utility maximization, might generate speculative bubbles and speculative chaos of the asset price.