Identifying critical financial networks of the DJIA: Toward a network‐based index

The purpose of this article is twofold. First, we introduce a novel definition of financial networks obtained from time series data from the stock market. Second, we demonstrate that these networks can be used as an index with the property to reflect critical states of the market, respectively, crashes sufficiently. Our work aims to advocate a network‐based analysis in the context of the stock market, because such a collective phenomenon can not only be economically described by networks but also analyzed as demonstrated in this article. © 2010 Wiley Periodicals, Inc. Complexity 16: 24–33, 2010     

欧式双向期权的两种定价比较

在股票价格服从泊松跳模型下,分别利用保险精算方法与无套利定价方法给出了欧式双向期权的定价公式;通过对这两种结果的比较发现,当股票价格服从特定的泊松跳模型时两种定价公式是相同的.     

一例系统性质改变导致的激变

当控制参数改变时，在一个受击台球模型中观察到从处处光滑保守系统向分段光滑类耗散系统的过渡。它导致标志典型保守随机网向系统函数不连续边界象集构成的瞬态随机网突然转变的特殊激变。瞬态随机网上的迭代最终落入一个由椭圆岛链形成的，在上述转变阈值出现的逃逸孔洞。这孔洞随控制参数增长而变大，使迭代逃逸更快，因此瞬态网上迭代的平均生存时间遵从具有特殊标度因子的幂律。与此同时，一个在同一阈值出现的肥分形禁区网也不断增长而且切掉原来保守随机网的越来越多的部分，使得剩余的瞬态网越来越“瘦”。我们的数值研究表示这一过程可以用另一个幂律来描述。     

A two-stage approach to multi-period allocation of savings among investment plans

This paper presents a two-stage multi-period decision model for allocation of the individual's savings into several investment plans. Although the U.S. economy is used as the background, the modelling methods are general enough to accommodate any tax law. The first stage of the model uses an asset-allocation method based on the single-index model. Because this method is static and does not provide for tax considerations and other constraints, it alone is not enough. The output of this optimal selection is used as exogenous parameters and controls for the second stage of the model which is an integer program. The IP includes fixed charges, statutory and budgetary constraints, a discount rate, and the risk level. We provide an example of this approach to illustrate how an individual can achieve his goals of terminal accumulations while maintaining the risk level, measured by the aggregate beta, he prefers. A linear programming relaxation of the IP model is utilized for sensitivity analysis to examine whether future adjustments in investment strategies are required. The model remains tractable enough for implementation by individuals who may not be experts in mathematical programming and financial planning.     

Hierarchical models and chaotic spin glasses

Renormalization-group studies in position space have led to the discovery of hierarchical models which are exactly solvable, exhibiting nonclassical critical behavior at finite temperature. Position-space renormalization-group approximations that had been widely and successfully used are in fact alternatively applicable as exact solutions of hierarchical models, this realizability guaranteeing important physical requirements. For example, a hierarchized version of the Sierpiriski gasket is presented, corresponding to a renormalization-group approximation which has quantitatively yielded the multicritical phase diagrams of submonolayers on graphite. Hierarchical models are now being studied directly as a testing ground for new concepts. For example, with the introduction of frustration, chaotic renormalization-group trajectories were obtained for the first time. Thus, strong and weak correlations are randomly intermingled at successive length scales, and a new microscopic picture and mechanism for a spin glass emerges. An upper critical dimension occurs via a boundary crisis mechanism in cluster-hierarchical variants developed to have well-behaved susceptibilities.     

Electrorheological properties of hydrolyzed poly(glycidyl methacrylate) suspensions

 Electrorheological behavior of silicone oil suspensions of macroporous poly[(glycidyl methacrylate)-co-(ethylene dimethacrylate)]) (0.60 : 0.40 w) hydrolyzed to various degrees was investigated. Polarizability of particles expressed by the particle dipole coefficient and, consequently, pseudoplasticity of the system at low shear rates after application of an external electric field steeply increased with the hydrolysis degree of the copolymer. As the size and shape of particles remain unchanged during hydrolysis, a series of model suspensions with the same hydrodynamic properties (Newtonian or slightly pseudoplastic when no electric field was applied) but with different intensity of the electrorheological effect could be prepared. Under these conditions, the use of Mason number failed to correlate the apparent viscosity of suspensions of particles with different polarizability in the electric field. On the other hand, when polarizability of particles of a suspension system changes due to a higher temperature, a single curve in the plot of apparent viscosity vs. the Mason number could be obtained. Received: 17 February 1998 Accepted: 8 May 1998     

Multi-scale correlations in different futures markets

In the present work we investigate the multiscale nature of the correlations for high frequency data (1 min) in different futures markets over a period of two years, starting on the 1st of January 2003 and ending on the 31st of December 2004. In particular, by using the concept of local Hurst exponent, we point out how the behaviour of this parameter, usually considered as a benchmark for persistency/antipersistency recognition in time series, is largely time-scale dependent in the market context. These findings are a direct consequence of the intrinsic complexity of a system where trading strategies are scale-adaptive. Moreover, our analysis points out different regimes in the dynamical behaviour of the market indices under consideration.     

Quantum modeling of nonlinear dynamics of stock prices: Bohmian approach

We use quantum mechanical methods to model the price dynamics in the financial market mathematically. We propose describing behavioral financial factors using the pilot-wave (Bohmian) model of quantum mechanics. The real price trajectories are determined (via the financial analogue of the second Newton law) by two financial potentials: the classical-like potential V (q) (“hard” market conditions) and the quantumlike potential U(q) (behavioral market conditions). Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 405–415, August, 2007.     

Generalized financial ratios

Ratios of random variables are prevalent in finance. Examples include: current ratio, sales margin, changes in capital employed, interest cover, liabilities ratio and financial leverage ratio. In this note, we derive the exact distribution of the ratio X/(X + Y) when X and Y are independent generalized Pareto random variables, Pareto distribution being the first and the most popular distribution used in finance. Copyright © 2007 John Wiley & Sons, Ltd.