9 research outputs found
Elements for a Theory of Financial Risks
Estimating and controlling large risks has become one of the main concern of
financial institutions. This requires the development of adequate statistical
models and theoretical tools (which go beyond the traditionnal theories based
on Gaussian statistics), and their practical implementation. Here we describe
three interrelated aspects of this program: we first give a brief survey of the
peculiar statistical properties of the empirical price fluctuations. We then
review how an option pricing theory consistent with these statistical features
can be constructed, and compared with real market prices for options. We
finally argue that a true `microscopic' theory of price fluctuations (rather
than a statistical model) would be most valuable for risk assessment. A simple
Langevin-like equation is proposed, as a possible step in this direction.Comment: 22 pages, to appear in `Order, Chance and Risk', Les Houches (March
1998), to be published by Springer/EDP Science
Diffusion entropy and waiting time statistics of hard x-ray solar flares
We analyze the waiting time distribution of time distances between two
nearest-neighbor flares. This analysis is based on the joint use of two
distinct techniques. The first is the direct evaluation of the distribution
function , or of the probability, , that no time
distance smaller than a given is found. We adopt the paradigm of the
inverse power law behavior, and we focus on the determination of the inverse
power index , without ruling out different asymptotic properties that
might be revealed, at larger scales, with the help of richer statistics. The
second technique, called Diffusion Entropy (DE) method, rests on the evaluation
of the entropy of the diffusion process generated by the time series. The
details of the diffusion process depend on three different walking rules, which
determine the form and the time duration of the transition to the scaling
regime, as well as the scaling parameter . With the first two rules the
information contained in the time series is transmitted, to a great extent, to
the transition, as well as to the scaling regime. The same information is
essentially conveyed, by using the third rules, into the scaling regime, which,
in fact, emerges very quickly after a fast transition process. We show that the
significant information hidden within the time series concerns memory induced
by the solar cycle, as well as the power index . The scaling parameter
becomes a simple function of , when memory is annihilated. Thus,
the three walking rules yield a unique and precise value of if the memory
is wisely taken under control, or cancelled by shuffling the data. All this
makes compelling the conclusion that .Comment: 23 pages, 13 figure
Characterization of the stretched exponential trap-time distributions in one-dimensional coupled map lattices
Stretched exponential distributions and relaxation responses are encountered
in a wide range of physical systems such as glasses, polymers and spin glasses.
As found recently, this type of behavior occurs also for the distribution
function of certain trap time in a number of coupled dynamical systems. We
analyze a one-dimensional mathematical model of coupled chaotic oscillators
which reproduces an experimental set-up of coupled diode-resonators and
identify the necessary ingredients for stretched exponential distributions.Comment: 8 pages, 8 figure
A reverse engineering approach to the suppression of citation biases reveals universal properties of citation distributions
The large amount of information contained in bibliographic databases has
recently boosted the use of citations, and other indicators based on citation
numbers, as tools for the quantitative assessment of scientific research.
Citations counts are often interpreted as proxies for the scientific influence
of papers, journals, scholars, and institutions. However, a rigorous and
scientifically grounded methodology for a correct use of citation counts is
still missing. In particular, cross-disciplinary comparisons in terms of raw
citation counts systematically favors scientific disciplines with higher
citation and publication rates. Here we perform an exhaustive study of the
citation patterns of millions of papers, and derive a simple transformation of
citation counts able to suppress the disproportionate citation counts among
scientific domains. We find that the transformation is well described by a
power-law function, and that the parameter values of the transformation are
typical features of each scientific discipline. Universal properties of
citation patterns descend therefore from the fact that citation distributions
for papers in a specific field are all part of the same family of univariate
distributions.Comment: 9 pages, 6 figures. Supporting information files available at
http://filrad.homelinux.or
A Comparison of On-Line Computer Science Citation Databases
Abstract. This paper examines the difference and similarities between the two on-line computer science citation databases DBLP and CiteSeer. The database entries in DBLP are inserted manually while the CiteSeer entries are obtained autonomously via a crawl of the Web and automatic processing of user submissions. CiteSeer’s autonomous citation database can be considered a form of self-selected on-line survey. It is important to understand the limitations of such databases, particularly when citation information is used to assess the performance of authors, institutions and funding bodies. We show that the CiteSeer database contains considerably fewer single author papers. This bias can be modeled by an exponential process with intuitive explanation. The model permits us to predict that the DBLP database covers approximately 24 % of the entire literature of Computer Science. CiteSeer is also biased against low-cited papers. Despite their difference, both databases exhibit similar and significantly different citation distributions compared with previous analysis of the Physics community. In both databases, we also observe that the number of authors per paper has been increasing over time.