Blackouts, risk, and fat-tailed distributions

We analyze a 19-year time series of North American electric power transmission system blackouts. Contrary to previously reported results we find a fatter than exponential decay in the distribution of inter- occurrence times and evidence of seasonal dependence in the number of events. Our findings question the use of self-organized criticality, and in particular the sandpile model, as a paradigm of blackout dynamics in power transmission systems. Hopefully, though, they will provide guidelines to more accurate models for evaluation of blackout risk.blackout, risk, fat-tailed distribution, power grid

Replacement of ensemble averaging by the use of a broadband source in scattering of light from a one-dimensional randomly rough interface between two dielectric media

By the use of phase perturbation theory we show that if a single realization of a one-dimensional randomly rough interface between two dielectric media is illuminated at normal incidence from either medium by a broadband Gaussian beam, it produces a scattered field whose differential reflection coefficient closely matches the result produced by averaging the differential reflection coefficient produced by a monochromatic incident beam over the ensemble of realizations of the interface profile function.Comment: 10 pages, 7 figure

Optimal Investment Horizons

In stochastic finance, one traditionally considers the return as a competitive measure of an asset, {\it i.e.}, the profit generated by that asset after some fixed time span $\Delta t$, say one week or one year. This measures how well (or how bad) the asset performs over that given period of time. It has been established that the distribution of returns exhibits ``fat tails'' indicating that large returns occur more frequently than what is expected from standard Gaussian stochastic processes (Mandelbrot-1967,Stanley1,Doyne). Instead of estimating this ``fat tail'' distribution of returns, we propose here an alternative approach, which is outlined by addressing the following question: What is the smallest time interval needed for an asset to cross a fixed return level of say 10%? For a particular asset, we refer to this time as the {\it investment horizon} and the corresponding distribution as the {\it investment horizon distribution}. This latter distribution complements that of returns and provides new and possibly crucial information for portfolio design and risk-management, as well as for pricing of more exotic options. By considering historical financial data, exemplified by the Dow Jones Industrial Average, we obtain a novel set of probability distributions for the investment horizons which can be used to estimate the optimal investment horizon for a stock or a future contract.Comment: Latex, 5 pages including 4 figur

Modeling highly volatile and seasonal markets: evidence from the Nord Pool electricity market

In this paper we address the issue of modeling spot electricity prices. After analyzing factors leading to the unobservable in other financial or commodity markets price dynamics we propose a mean reverting jump diffusion model. We fit the model to data from the Nord Pool power exchange and find that it nearly duplicates the spot price's main characteristics. The model can thus be used for risk management and pricing derivatives written on the spot electricity price.electricity price, mean reversion, wavelet transform, jump diffusion model

Inverse Statistics in Economics : The gain-loss asymmetry

Inverse statistics in economics is considered. We argue that the natural candidate for such statistics is the investment horizons distribution. This distribution of waiting times needed to achieve a predefined level of return is obtained from (often detrended) historic asset prices. Such a distribution typically goes through a maximum at a time called the {\em optimal investment horizon}, $\tau^*_\rho$, since this defines the most likely waiting time for obtaining a given return $\rho$. By considering equal positive and negative levels of return, we report on a quantitative gain-loss asymmetry most pronounced for short horizons. It is argued that this asymmetry reflects the market dynamics and we speculate over the origin of this asymmetry.Comment: Latex, 6 pages, 3 figure