26,539 research outputs found
Price Variations in a Stock Market With Many Agents
Large variations in stock prices happen with sufficient frequency to raise
doubts about existing models, which all fail to account for non-Gaussian
statistics. We construct simple models of a stock market, and argue that the
large variations may be due to a crowd effect, where agents imitate each
other's behavior. The variations over different time scales can be related to
each other in a systematic way, similar to the Levy stable distribution
proposed by Mandelbrot to describe real market indices. In the simplest, least
realistic case, exact results for the statistics of the variations are derived
by mapping onto a model of diffusing and annihilating particles, which has been
solved by quantum field theory methods. When the agents imitate each other and
respond to recent market volatility, different scaling behavior is obtained. In
this case the statistics of price variations is consistent with empirical
observations. The interplay between ``rational'' traders whose behavior is
derived from fundamental analysis of the stock, including dividends, and
``noise traders'', whose behavior is governed solely by studying the market
dynamics, is investigated. When the relative number of rational traders is
small, ``bubbles'' often occur, where the market price moves outside the range
justified by fundamental market analysis. When the number of rational traders
is larger, the market price is generally locked within the price range they
define.Comment: 39 pages (Latex) + 20 Figures and missing Figure 1 (sorry), submitted
to J. Math. Eco
Invisible control of self-organizing agents leaving unknown environments
In this paper we are concerned with multiscale modeling, control, and
simulation of self-organizing agents leaving an unknown area under limited
visibility, with special emphasis on crowds. We first introduce a new
microscopic model characterized by an exploration phase and an evacuation
phase. The main ingredients of the model are an alignment term, accounting for
the herding effect typical of uncertain behavior, and a random walk, accounting
for the need to explore the environment under limited visibility. We consider
both metrical and topological interactions. Moreover, a few special agents, the
leaders, not recognized as such by the crowd, are "hidden" in the crowd with a
special controlled dynamics. Next, relying on a Boltzmann approach, we derive a
mesoscopic model for a continuum density of followers, coupled with a
microscopic description for the leaders' dynamics. Finally, optimal control of
the crowd is studied. It is assumed that leaders exploit the herding effect in
order to steer the crowd towards the exits and reduce clogging. Locally-optimal
behavior of leaders is computed. Numerical simulations show the efficiency of
the optimization methods in both microscopic and mesoscopic settings. We also
perform a real experiment with people to study the feasibility of the proposed
bottom-up crowd control technique.Comment: in SIAM J. Appl. Math, 201
A simple Monte Carlo model for crowd dynamics
In this paper we introduce a simple Monte Carlo method for simulating the
dynamics of a crowd. Within our model a collection of hard-disk agents is
subjected to a series of two-stage steps, implying (i) the displacement of one
specific agent followed by (ii) a rearrangement of the rest of the group
through a Monte Carlo dynamics. The rules for the combined steps are determined
by the specific setting of the granular flow, so that our scheme should be
easily adapted to describe crowd dynamics issues of many sorts, from stampedes
in panic scenarios to organized flow around obstacles or through bottlenecks.
We validate our scheme by computing the serving times statistics of a group of
agents crowding to be served around a desk. In the case of a size homogeneous
crowd, we recover intuitive results prompted by physical sense. However, as a
further illustration of our theoretical framework, we show that heterogeneous
systems display a less obvious behavior, as smaller agents feature shorter
serving times. Finally, we analyze our results in the light of known properties
of non-equilibrium hard-disk fluids and discuss general implications of our
model.Comment: to be published in Physical Review
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