73,949 research outputs found
Critical Relaxation and Critical Exponents
Dynamic relaxation of the XY model and fully frustrated XY model quenched
from an initial ordered state to the critical temperature or below is
investigated with Monte Carlo methods. Universal power law scaling behaviour is
observed. The dynamic critical exponent and the static exponent are
extracted from the time-dependent Binder cumulant and magnetization. The
results are competitive to those measured with traditional methods
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 Characterization of Subspaces and Quotients of Reflexive Banach Spaces with Unconditional Bases
We prove that the dual or any quotient of a separable reflexive Banach space
with the unconditional tree property has the unconditional tree property. Then
we prove that a separable reflexive Banach space with the unconditional tree
property embeds into a reflexive Banach space with an unconditional basis. This
solves several long standing open problems. In particular, it yields that a
quotient of a reflexive Banach space with an unconditional finite dimensional
decomposition embeds into a reflexive Banach space with an unconditional basis
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