361 research outputs found
Colored minority games
We study the behavior of simple models for financial markets with widely
spread frequency either in the trading activity of agents or in the occurrence
of basic events. The generic picture of a phase transition between information
efficient and inefficient markets still persists even when agents trade on
widely spread time-scales. We derive analytically the dependence of the
critical threshold on the distribution of time-scales. We also address the
issue of market efficiency as a function of frequency. In an inefficient market
we find that the size of arbitrage opportunities is inversely proportional to
the frequency of the events on which they occur. Greatest asymmetries in market
outcomes are concentrated on the most rare events. The practical limits of the
applications of these ideas to real markets are discussed in a specific
example.Comment: 15 pages, 3 figure
On information efficiency and financial stability
We study a simple model of an asset market with informed and non-informed
agents. In the absence of non-informed agents, the market becomes information
efficient when the number of traders with different private information is
large enough. Upon introducing non-informed agents, we find that the latter
contribute significantly to the trading activity if and only if the market is
(nearly) information efficient. This suggests that information efficiency might
be a necessary condition for bubble phenomena, induced by the behavior of
non-informed traders, or conversely that throwing some sands in the gears of
financial markets may curb the occurrence of bubbles.Comment: 14 pages, 2 figure
Criticality of mostly informative samples: A Bayesian model selection approach
We discuss a Bayesian model selection approach to high dimensional data in
the deep under sampling regime. The data is based on a representation of the
possible discrete states , as defined by the observer, and it consists of
observations of the state. This approach shows that, for a given sample
size , not all states observed in the sample can be distinguished. Rather,
only a partition of the sampled states can be resolved. Such partition
defines an {\em emergent} classification of the states that becomes finer
and finer as the sample size increases, through a process of {\em symmetry
breaking} between states. This allows us to distinguish between the
of a given representation of the observer defined states ,
which is given by the entropy of , and its which is defined by
the entropy of the partition . Relevance has a non-monotonic dependence on
resolution, for a given sample size. In addition, we characterise most relevant
samples and we show that they exhibit power law frequency distributions,
generally taken as signatures of "criticality". This suggests that
"criticality" reflects the relevance of a given representation of the states of
a complex system, and does not necessarily require a specific mechanism of
self-organisation to a critical point.Comment: 31 pages, 7 figure
Self Organization of Interacting Polya Urns
We introduce a simple model which shows non-trivial self organized critical
properties. The model describes a system of interacting units, modelled by
Polya urns, subject to perturbations and which occasionally break down. Three
equivalent formulations - stochastic, quenched and deterministic - are shown to
reproduce the same dynamics. Among the novel features of the model are a
non-homogeneous stationary state, the presence of a non-stationary critical
phase and non-trivial exponents even in mean field. We discuss simple
interpretations in term of biological evolution and earthquake dynamics and we
report on extensive numerical simulations in dimensions as well as in
the random neighbors limit.Comment: 4 pages 1 figur
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