9,325 research outputs found
A Model of Market Limit Orders By Stochastic PDE's, Parameter Estimation, and Investment Optimization
In this paper we introduce a completely continuous and time-variate model of
the evolution of market limit orders based on the existence, uniqueness, and
regularity of the solutions to a type of stochastic partial differential
equations obtained in Zheng and Sowers (2012). In contrary to several models
proposed and researched in literature, this model provides complete continuity
in both time and price inherited from the stochastic PDE, and thus is
particularly suitable for the cases where transactions happen in an extremely
fast pace, such as those delivered by high frequency traders (HFT's).
We first elaborate the precise definition of the model with its associated
parameters, and show its existence and uniqueness from the related mathematical
results given a fixed set of parameters. Then we statistically derive parameter
estimation schemes of the model using maximum likelihood and least
mean-square-errors estimation methods under certain criteria such as AIC to
accommodate to variant number of parameters . Finally as a typical economics
and finance use case of the model we settle the investment optimization problem
in both static and dynamic sense by analysing the stochastic (It\^{o})
evolution of the utility function of an investor or trader who takes the model
and its parameters as exogenous. Two theorems are proved which provide criteria
for determining the best (limit) price and time point to make the transaction
A method for getting a finite in the IR region from an all-order beta function
The analytical method of QCD running coupling constant is extended to a model
with an all-order beta function which is inspired by the famous
Novikov-Shifman-Vai\-n\-s\-htein-Zakharov beta function of N=1 supersymmetric
gau\-g\-e theories. In the approach presented here, the running coupling is
determined by a transcendental equation with non-elementary integral of the
running scale . In our approach , which reads 0.30642,
does not rely on any dimensional parameters. This is in accordance with results
in the literature on the analytical method of QCD running coupling constant.
The new "analytically im\-p\-roved" running coupling constant is also
compatible with the property of asymptotic freedom.Comment: 5 pages, 3 figure
Background field method in the large expansion of scalar QED
Using the background field method, we, in the large approximation,
calculate the beta function of scalar quantum electrodynamics at the first
nontrivial order in by two different ways. In the first way, we get the
result by summing all the graphs contributing directly. In the second way, we
begin with the Borel transform of the related two point Green's function. The
main results are that the beta function is fully determined by a simple
function and can be expressed as an analytic expression with a finite radius of
convergence, and the scheme-dependent renormalized Borel transform of the two
point Green's function suffers from renormalons.Comment: 13 pages, 4 figures, 1 table, to appear in the European Physical
Journal
Magnetic field twist driven by remote convective motions: Characteristics and twist rates
It is generally believed that convective motions below the solar photosphere induce a twist in the coronal magnetic field as a result of frozen-in physics. A question of interest is how much twist can one expect from a persistent convective motion, given the fact that dissipative effects will eventually figure. This question is examined by considering a model problem: two conducting plates, with finite resistivity, are set in sheared motion and forced at constant relative speed. A resistive plasma is between the plates and an initially vertical magnetic field connects the plates. The time rate of tilt experienced by the field is obtained as a function of Hartmann number and the resistivity ratio. Both analytical and numerical approaches are considered
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