We demonstrate that high-level file system events exhibit self-similar behaviour, but only for short-term time scales of approximately under a day. We do so through the analysis of four sets of traces that span time scales of milliseconds through months, and that differ in the trace collection method, the file systems being traced, and the chronological times of the tracing. Two sets of detailed, short-term file system trace data are analyzed; both are shown to have self-similar like behaviour, with consistent Hurst parameters (a measure of self-similarity) for all file system traffic as well as individual classes of file system events. Long-term file system trace data is then analyzed, and we discover that the traces' high variability and self-similar behaviour does not persist across time scales of days, weeks, and months. Using the short-term trace data, weshow that sources of file system traffic exhibit ON/OFF source behaviour, which is characterized by highly variably lengthed bursts of activity, followed by similarly variably lengthed periods of inactivity. This ON/OFF behaviour is used to motivate a simple technique for synthesizing a stream of events that exhibit the same self-similar short-term behaviour as was observed in the file system traces.

this paper I shall make a case for a dynamic semiotics. I list a set of phenomena that are difficult to understand in standard theories, and suggest a model borrowed from theories of complex dynamic systems. Since such theories rely on processes of self-organization that often defy analytical treatment, I use small computational models for assessing the empirical consequences of the theories.

Increases in market volatility of asset prices have been observed and analyzed in recent years and their cause has generally been attributed to the popularity of portfolio insurance strategies for derivative securities. The basis of derivative pricing is the Black-Scholes model and its use is so extensive that it is likely to influence the market itself. In particular it has been suggested that this is a factor in the rise in volatilities. In this work we present a class of pricing models that account for the feedback effect from the Black-Scholes dynamic hedging strategies on the price of the asset, and from there back onto the price of the derivative. These models do predict increased implied volatilities with minimal assumptions beyond those of the Black-Scholes theory. They are characterized by a nonlinear partial differential equation that reduces to the Black-Scholes equation when the feedback is removed. We begin with a model economy consisting of two distinct groups of traders: Reference traders who are the majority investing in the asset expecting gain, and program traders who trade the asset following a Black-Scholes type dynamic hedging strategy, which is not known a priori, in order to insure against the risk of a derivative security. The interaction of these groups leads to a stochastic process for the price of the asset which depends on the hedging strategy of the program traders. Then following a Black-Scholes argument, we

Artificial neural networks are increasingly popular in today's business fields. They have been hailed as the greatest technological advance since the invention of transistors. The purpose of this paper is to answer two of the most frequently asked questions: "What are neural networks? " "Why are they so popular in today's business fields? " The paper reviews the common characteristics of neural networks and discusses the feasibility of neuralnet applications in business fields. It then presents four actual application cases and identifies the limitations of the current neural-net technology.

We describe an end-to-end real-time S&P futures trading system. Inner-shell stochastic nonlinear dynamic models are developed, and Canonical Momenta Indicators (CMI) are derived from a fitted Lagrangian used by outer-shell trading models dependent on these indicators. Recursive and adaptive optimization using Adaptive Simulated Annealing (ASA) is used for fitting parameters shared across these shells of dynamic and trading models.

The volatility of a financial asset is the variance per unit time of the logarithm of the price of the asset. Volatility has a key role to play in the determination of risk and in the valuation of options and other derivative securities. The widespread Black-Scholes model for asset prices assumes constant volatility. The purpose of this chapter is to review the evidence for non-constant volatility and to consider the implications for option pricing of alternative random or stochastic volatility models. We concentrate on continuous time diffusion models for the volatility, but we also make comments about certain classes of discrete time models, such as ARV, ARCH and GARCH. 1 Volatility and the need for Stochastic Volatility models 1.1 Introduction A common approach in the modelling of financial assets is to assume that the proportional price changes of an asset form a Gaussian process with stationary independent increments. The celebrated (and ubiquitous) Black-Scholes option pricin...

this paper I offer some ideas of possible ways of doing this. I shall use two types of dynamic models, Thom's catastrophe theory already mentioned and the formalism of cellular automata. In addition, I shall use the theory of autopoiesis developed by N. Luhmann, H. Maturana, F. Varela, and others as the general framework in which the formal ideas are developed.

High frequency DEM-USD exchange rate data (resolution > 2 seconds) are analyzed for their scaling behavior as a function of the time lag. Motivated by the finding that the distribution of 1-quote returns is rather insensitive to the physical time duration between successive quotes, lags are measured in units of quotes. The mean absolute returns over lags of different sizes, shows three different regimes. The smallest time scales show no scaling, followed by two scaling regimes characterized by Hurst exponents H = 0.45 and H = 0.56, with a crossover occuring at lags of # 500 quotes. The up-down correlation coefficient, defined here, shows strong anticorrelations on scales smaller than 500. The lack of convergence to a large deviation rate function, convex tails in the logarithm of the probability distributions, strong up-down correlations and H < 0.5, show that the dynamics on small scales is more complicated than random walk models with i.i.d. increments. Nevertheless, for both scaling re...

The price of financial assets are, since [1], considered to be described by a (discrete or continuous) time sequence of random variables, i.e a stochastic process. Sharp scaling exponents or unifractal behavior of such processes has been reported in several works [2] [3] [4] [5] [6]. In this letter we investigate the question of scaling transformation of price processes by establishing a new connexion between nonlinear group theoretical methods and multifractal methods developed in mathematical physics. Using two sets of financial chronological time series, we show that the scaling transformation is a non-linear group action on the moments of the price increments. Its linear part has a spectral decomposition that puts in evidence a multifractal behavior of the price increments. 1

Recent analysis of real network traffic has shown that a large number of traffic sources produces a traffic stream that is self-similar over several time scales. Motivated by this observation a high-speed Asynchronous Transfer Mode (ATM) traffic generator based on fractional Brownian motion is presented. The traffic simulator generates call arrivals as well as the desired traffic parameters for each call. It is therefore an ideal tool to analyze a wide spectrum of networking functions such as switch performance, routing, and call admission control algorithms. The presented algorithm can be highly parallelized, thus generating traffic logs in a period several orders of magnitude below the actual simulated time period. 1 Introduction In many different areas where long time series [Taq86] are available, certain correlation structures have been observed that manifest a self-similar (fractal) character. To give a few examples: ffl Hydrology [Man65, Hur51], the study of the amount of dail...