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1.
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We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale.  相似文献   

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We derive a closed-form solution for the price of an average strike as well as an average price geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is approximate when the correlation increases.  相似文献   

5.
An ecological economic model of trawling is presented to demonstrate the effect of trawling location choice strategy on net input (rate of economic gain of fish caught per time spent less costs). Fishing location choice is considered to be a dynamic process whereby trawlers chose from among a repertoire of plastic strategies that they modify if their gains fall below a fixed proportion of the mean gains of the fleet as a whole. The distribution of fishing across different areas of a fishery follows an approximate ideal free distribution (IFD) with varying noise due to uncertainty. The least-productive areas are not utilised because initial net input never reaches the mean yield of better areas subject to competitive exploitation. In cases, where there is a weak temporal autocorrelation between fish stocks in a specific location, a plastic strategy of local translocation between trawls mixed with longer-range translocation increases realised input. The trawler can change its translocation strategy in the light of information about recent trawling success compared to its long-term average but, in contrast to predictions of the Marginal Value Theorem (MVT) model, does not know for certain what it will find by moving, so may need to sample new patches. The combination of the two types of translocation mirrored beam-trawling strategies used by the Dutch fleet and the resultant distribution of trawling effort is confirmed by analysis of historical effort distribution of British otter trawling fleets in the North Sea. Fisheries exploitation represents an area where dynamic agent-based adaptive models may be a better representation of the economic dynamics of a fleet than classically inspired optimisation models.  相似文献   

6.
Time-varying Hurst exponent for US stock markets   总被引:2,自引:0,他引:2  
In this work, the dynamical behavior of the US stock markets is characterized on the basis of the temporal variations of the Hurst exponent estimated with detrended fluctuation analysis (DFA) over moving windows for the historical Dow Jones (1928-2007) and the S&P-500 (1950-2007) daily indices. According to the results drawn: (i) the Hurst exponent displays an erratic dynamics with some episodes alternating low and high persistent behavior, (ii) the major breakthrough of the long-term trend of the scaling behavior occurred in 1972, at the end of the Bretton Woods system, when the Hurst exponent shifted form a positive to a negative long-term trend. Other effects, such as the 1987 crisis and the emergence of anti-correlated behavior in the recent two years, are also discussed.  相似文献   

7.
We examine possible closed form solutions for the cumulative distribution function for systems where the probability density function can be adequately described by the generalized non-extensive statistics framework. Application to financial time series as a possible Value at Risk technique indicates reasonable agreement with the data under consideration, including all possible extremes and asymmetries of the returns. Numerical results to illustrate the efficiency of the method are presented.  相似文献   

8.
Soon-Hyung Yook  Yup Kim 《Physica A》2008,387(26):6605-6612
We study two weight-driven information spreading models for financial market. In these models, we find that the activity threshold below which the ‘financial crash’ occurs can be increased by uneven distribution of information weight, compared with Eguíluz and Zimmermann model [V.M. Eguíluz, M.G. Zimmermann, Phys. Rev. Lett. 85 (2000) 5659]. We also find that below the threshold the normalized return distribution, P(Z;Δt) satisfies P(Z=0;Δt)∼exp(−Δt/b) whereas P(Z=0;Δt)∼Δtτ above the threshold. Here Δt is the time interval where the normalized return is defined, Z(t,Δt)=Z(t+Δt)−Z(t). By approximating the relative increase of P(Z;Δt=1) for large Z as Gaussian distribution with non-zero mean, we show that the non-zero mean of the Gaussian distribution can cause such exponentially decaying behavior of P(Z=0;Δt).  相似文献   

9.
There are various ways of quantifying the statistical heterogeneity of a given probability law: Statistics uses variance — which measures the law’s dispersion around its mean; Physics and Information Theory use entropy — which measures the law’s randomness; Economics uses the Gini index — which measures the law’s egalitarianism. In this research we explore an alternative to the Gini index-the Pietra index-which is a counterpart of the Kolmogorov-Smirnov statistic. The Pietra index is shown to be a natural and elemental measure of statistical heterogeneity, which is especially useful in the case of asymmetric and skewed probability laws, and in the case of asymptotically Paretian laws with finite mean and infinite variance. Moreover, the Pietra index is shown to have immediate and fundamental interpretations within the following applications: renewal processes and continuous time random walks; infinite-server queueing systems and shot noise processes; financial derivatives. The interpretation of the Pietra index within the context of financial derivatives implies that derivative markets, in effect, use the Pietra index as their benchmark measure of statistical heterogeneity.  相似文献   

10.
Trading model with pair pattern strategies   总被引:1,自引:0,他引:1  
F. Ren  Y.C. Zhang 《Physica A》2008,387(22):5523-5534
A simple trading model based on pair pattern strategy space with holding periods is proposed. Power-law behavior is observed for the return variance σ2, the price impact H and the predictability K for both models, with linear and square root impact functions. The sum of the traders’ wealth displays a positive value for the model with a square root price impact function, and a qualitative explanation is given based on the observation of the conditional excess demand 〈A|u〉. The cumulative wealth distribution also obeys a power-law behavior with an exponent close to that of real markets. An evolutionary trading model is further proposed. The elimination mechanism effectively changes the behavior of traders, and a power-law behavior is observed in the measure of zero return distribution P(r=0). The trading model with other types of traders, e.g., traders with the MG’s strategies and producers, are also carefully studied.  相似文献   

11.
In this paper we propose a model of electricity market based on the forward rate dynamics described by a diffusion with jumps as a generalization of the classical diffusion approach. We consider jump components resulting from a coupled continuous-time random walk (CTRW) with jump lengths proportional to the corresponding inter-jump time intervals. In the framework of the model we derive a formula for the EURO-price of a standard European call option, showing applicability of CTRW processes for pricing of financial instruments. The result, obtained by an advance theory of semimartingales, is an essential extension of the pricing formula derived in the classical diffusion model of the forward rate dynamics. It indicates an influence of both, the continuous and the jump parts of the forward rate process on the option price.  相似文献   

12.
H.F. Chau  V.H. Chan  F.K. Chow 《Physica A》2008,387(23):5874-5886
Hypothesis Testing Minority Game (HMG) is a variant of the standard Minority Game (MG) that models the inertial behavior of agents in the market. In the earlier study of our group, we find that agents cooperate better in HMG than in the standard MG when strategies are picked from the full strategy space. Here we continue to study the behavior of HMG when strategies are chosen from the maximal reduced strategy space. Surprisingly, we find that, unlike the standard MG, the level of cooperation in HMG depends strongly on the strategy space used. In addition, a novel intermittency dynamics is also observed in the minority choice time series in a certain parameter range in which the orderly phases are characterized by a variety of periodic dynamics. Remarkably, all these findings can be explained by the crowd-anticrowd theory.  相似文献   

13.
Y.C. Ni  P.M. Hui 《Physica A》2009,388(23):4856-4862
An evolutionary snowdrift game (SG) that incorporates bounded rationality and limited information in the evolutionary process is proposed and studied. Based on SG in a well-mixed population and defining the winning action at a turn to be the one that gets a higher payoff, the most recent m winning actions can be used as a public information based on which the competing agents decide their next actions. This defines a strategy pool from which each agent picks a number of strategies as their tool in adapting to the competing environment. The payoff parameter r in SG serves to set the maximum number of winners per turn. Due to the bounded rationality and limited information, the cooperative frequency shows steps and plateaux as a function of r and these features tend to be smoothed out as m increases. These features are results of an interplay between a restricted subset of m-bit histories that the system can visit at a value of r and the limited capacity that agents can adapt. The standard deviation in the number of agents taking the cooperative action is also studied. For general values of r, our model generates a realization of the binary-agent-resource model. The idea of introducing bounded rationality into a two-person game to realize the minority game or binary-agent-resource model could be a useful tool for future research.  相似文献   

14.
Wen-Bo Du  Mao-Bin Hu 《Physica A》2008,387(14):3796-3800
This paper investigates the evolutionary prisoner’s dilemma on weighted scale-free networks. The weighted networks are generated by adopting Barabási-Albert scale-free network and assigning link weight with wij=(ki×kj)β. Simulation results show that the cooperation frequency has a strong dependence on β. The value of β which is associated with the maximal cooperation frequency has been sought out. Moreover, Gini coefficient and Pareto exponent of the system’s wealth distribution are investigated. The inequality of wealth distribution is minimized at β≈−1.  相似文献   

15.
Lev Muchnik  Shlomo Havlin 《Physica A》2009,388(19):4145-4150
It is well known that while daily price returns of financial markets are uncorrelated, their absolute values (‘volatility’) are long-term correlated. Here we provide evidence that certain subsequences of the returns themselves also exhibit long-term memory. These subsequences consist of maxima (or minima) of returns in consecutive time windows of R days. Our analysis shows that for both stocks and currency exchange rates, long-term correlations are significant for R≥4. We argue that this long-term memory which is similar to that observed in volatility clustering sheds further insight on price dynamics that might be used for risk estimation.  相似文献   

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17.
Naoya Sazuka  Jun-ichi Inoue 《Physica A》2009,388(14):2839-2853
Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely a distribution derived from the Mittag-Leffler survival function and the Weibull distribution. For the Mittag-Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter tmax, whereas the results based on the Weibull distribution do not depend on such a cut-off. Therefore, a Weibull distribution is more convenient than a Mittag-Leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other hand, we find that the Gini index is rather independent of the cut-off parameter. Based on the above considerations, we propose a good candidate for describing the distribution of first-passage time in a market: The Weibull distribution with a power-law tail. This distribution compensates the gap between theoretical and empirical results more efficiently than a simple Weibull distribution. It should be stressed that a Weibull distribution with a power-law tail is more flexible than the Mittag-Leffler distribution, which itself can be approximated by a Weibull distribution and a power-law. Indeed, the key point is that in the former case there is freedom of choice for the exponent of the power-law attached to the Weibull distribution, which can exceed 1 in order to reproduce decays faster than possible with a Mittag-Leffler distribution. We also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory. Moreover, we discuss the limitation of our distributions by applying our distribution to the analysis of the BTP future and calculating the average waiting time. We find that our distribution is applicable as long as durations follow a Weibull law for short times and do not have too heavy a tail.  相似文献   

18.
Aki-Hiro Sato 《Physica A》2008,387(15):3960-3966
Empirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi-dimensional time series with spectral distances introduced in [A.-H. Sato, Physica A 382 (2007) 258-270]. As a result it is found that the similarities among currency pairs fluctuate with the rotation of the earth, and that the similarities among best quotation rates are associated with those among quotation frequencies. Furthermore, it is shown that the Jensen-Shannon spectral divergence is proportional to a mean of the Kullback-Leibler spectral distance both empirically and numerically. It is confirmed that these spectral distances are connected with distributions for behavioural parameters of the market participants from numerical simulation. This concludes that spectral distances of representative quantities of financial markets are related into diversification of behavioural parameters of the market participants.  相似文献   

19.
Li Ma 《Physics letters. A》2009,373(25):2154-2161
In this Letter, the mean-square exponential stability problem for stochastic Hopfield neural networks with both discrete and distributed time-varying delays is investigated. By choosing a modified Lyapunov-Krasovskii functional, a delay-dependent criterion is established such that the stochastic neural network is mean-square exponentially stable. The derivative of discrete time-varying delay h(t) satisfies and the decay rate β can be any finite positive value without any other constraints. The assumptions given in this Letter are more general than the conventional assumptions (i.e., and β satisfies a transcendental equation or an inequality). Finally, numerical examples are provided to illustrate the effectiveness of the proposed sufficient conditions.  相似文献   

20.
Xinghua Liu  Shirley Gregor 《Physica A》2008,387(11):2535-2546
Recent literature has developed the conjecture that important statistical features of stock price series, such as the fat tails phenomenon, may depend mainly on the market microstructure. This conjecture motivated us to investigate the roles of both the market microstructure and agent behavior with respect to high-frequency returns and daily returns. We developed two simple models to investigate this issue. The first one is a stochastic model with a clearing house microstructure and a population of zero-intelligence agents. The second one has more behavioral assumptions based on Minority Game and also has a clearing house microstructure. With the first model we found that a characteristic of the clearing house microstructure, namely the clearing frequency, can explain fat tail, excess volatility and autocorrelation phenomena of high-frequency returns. However, this feature does not cause the same phenomena in daily returns. So the Stylized Facts of daily returns depend mainly on the agents’ behavior. With the second model we investigated the effects of behavioral assumptions on daily returns. Our study implicates that the aspects which are responsible for generating the stylized facts of high-frequency returns and daily returns are different.  相似文献   

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