32,425 research outputs found
Mean Field Limit of a Behavioral Financial Market Model
In the past decade there has been a growing interest in agent-based
econophysical financial market models. The goal of these models is to gain
further insights into stylized facts of financial data. We derive the mean
field limit of the econophysical model by Cross, Grinfeld, Lamba and Seaman
(Physica A, 354) and show that the kinetic limit is a good approximation of the
original model. Our kinetic model is able to replicate some of the most
prominent stylized facts, namely fat-tails of asset returns, uncorrelated stock
price returns and volatility clustering. Interestingly, psychological
misperceptions of investors can be accounted to be the origin of the appearance
of stylized facts. The mesoscopic model allows us to study the model
analytically. We derive steady state solutions and entropy bounds of the
deterministic skeleton. These first analytical results already guide us to
explanations for the complex dynamics of the model
StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer
We present a simple method to solve spherical harmonics moment systems, such
as the the time-dependent and equations, of radiative transfer.
The method, which works for arbitrary moment order , makes use of the
specific coupling between the moments in the equations. This coupling
naturally induces staggered grids in space and time, which in turn give rise to
a canonical, second-order accurate finite difference scheme. While the scheme
does not possess TVD or realizability limiters, its simplicity allows for a
very efficient implementation in Matlab. We present several test cases, some of
which demonstrate that the code solves problems with ten million degrees of
freedom in space, angle, and time within a few seconds. The code for the
numerical scheme, called StaRMAP (Staggered grid Radiation Moment
Approximation), along with files for all presented test cases, can be
downloaded so that all results can be reproduced by the reader.Comment: 28 pages, 7 figures; StaRMAP code available at
http://www.math.temple.edu/~seibold/research/starma
Metric entropy, n-widths, and sampling of functions on manifolds
We first investigate on the asymptotics of the Kolmogorov metric entropy and
nonlinear n-widths of approximation spaces on some function classes on
manifolds and quasi-metric measure spaces. Secondly, we develop constructive
algorithms to represent those functions within a prescribed accuracy. The
constructions can be based on either spectral information or scattered samples
of the target function. Our algorithmic scheme is asymptotically optimal in the
sense of nonlinear n-widths and asymptotically optimal up to a logarithmic
factor with respect to the metric entropy
The Repurchase Behavior of Individual Investors: An Experimental Investigation
We analyze two recently documented follow-on purchase and repurchase patterns experimentally: Individual investors’ preference for purchasing additional shares of a stock that decreased rather than increased in value succeeding an initial purchase (pattern 1) and investors’ tendency for purchasing stocks that they previously sold at a higher price (pattern 2). Similar to the field data study by Odean, Strahilevitz, and Barber (2004), subjects in our experiment are about 2.5 to 3 times as likely to purchase units of a single fictitious good if the price of the good declined following a purchase or sale in the previous period. As an assignment of choices clearly reduces the effect, we ar-gue that investors are involved in counterfactual thinking: They refrain from purchasing additional shares or repurchasing shares at a higher price because doing so means admitting to their ex post wrong decision.
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