3,701 research outputs found
Agent-based model with asymmetric trading and herding for complex financial systems
Background: For complex financial systems, the negative and positive
return-volatility correlations, i.e., the so-called leverage and anti-leverage
effects, are particularly important for the understanding of the price
dynamics. However, the microscopic origination of the leverage and
anti-leverage effects is still not understood, and how to produce these effects
in agent-based modeling remains open. On the other hand, in constructing
microscopic models, it is a promising conception to determine model parameters
from empirical data rather than from statistical fitting of the results.
Methods: To study the microscopic origination of the return-volatility
correlation in financial systems, we take into account the individual and
collective behaviors of investors in real markets, and construct an agent-based
model. The agents are linked with each other and trade in groups, and
particularly, two novel microscopic mechanisms, i.e., investors' asymmetric
trading and herding in bull and bear markets, are introduced. Further, we
propose effective methods to determine the key parameters in our model from
historical market data.
Results: With the model parameters determined for six representative
stock-market indices in the world respectively, we obtain the corresponding
leverage or anti-leverage effect from the simulation, and the effect is in
agreement with the empirical one on amplitude and duration. At the same time,
our model produces other features of the real markets, such as the fat-tail
distribution of returns and the long-term correlation of volatilities.
Conclusions: We reveal that for the leverage and anti-leverage effects, both
the investors' asymmetric trading and herding are essential generation
mechanisms. These two microscopic mechanisms and the methods for the
determination of the key parameters can be applied to other complex systems
with similar asymmetries.Comment: 17 pages, 6 figure
Quantum Game with Restricted Matrix Strategies
We study a quantum game played by two players with restricted multiple
strategies. It is found that in this restricted quantum game Nash equilibrium
does not always exist when the initial state is entangled. At the same time, we
find that when Nash equilibrium exists the pay off function is usually
different from that in the classical counterpart except in some special cases.
This presents an explicit example where quantum game and classical game may
differ. When designing a quantum game with limited strategies, the allowed
strategy should be carefully chosen according to the type of initial state.Comment: 5 pages and 3 figure
Unipotent representations of real classical groups
Let be a complex orthogonal or complex symplectic group, and let
be a real form of , namely is a real orthogonal group, a
real symplectic group, a quaternionic orthogonal group, or a quaternionic
symplectic group. For a fixed parity , we
define a set of nilpotent
-orbits in (the Lie algebra of ). When
is the parity of the dimension of the standard module of , this is the set of the stably trivial special nilpotent orbits, which
includes all rigid special nilpotent orbits. For each , we construct all unipotent
representations of (or its metaplectic cover when is a real symplectic
group and is odd) attached to via the method of theta
lifting and show in particular that they are unitary
Gibbs Max-margin Topic Models with Data Augmentation
Max-margin learning is a powerful approach to building classifiers and
structured output predictors. Recent work on max-margin supervised topic models
has successfully integrated it with Bayesian topic models to discover
discriminative latent semantic structures and make accurate predictions for
unseen testing data. However, the resulting learning problems are usually hard
to solve because of the non-smoothness of the margin loss. Existing approaches
to building max-margin supervised topic models rely on an iterative procedure
to solve multiple latent SVM subproblems with additional mean-field assumptions
on the desired posterior distributions. This paper presents an alternative
approach by defining a new max-margin loss. Namely, we present Gibbs max-margin
supervised topic models, a latent variable Gibbs classifier to discover hidden
topic representations for various tasks, including classification, regression
and multi-task learning. Gibbs max-margin supervised topic models minimize an
expected margin loss, which is an upper bound of the existing margin loss
derived from an expected prediction rule. By introducing augmented variables
and integrating out the Dirichlet variables analytically by conjugacy, we
develop simple Gibbs sampling algorithms with no restricting assumptions and no
need to solve SVM subproblems. Furthermore, each step of the
"augment-and-collapse" Gibbs sampling algorithms has an analytical conditional
distribution, from which samples can be easily drawn. Experimental results
demonstrate significant improvements on time efficiency. The classification
performance is also significantly improved over competitors on binary,
multi-class and multi-label classification tasks.Comment: 35 page
Discriminative Nonparametric Latent Feature Relational Models with Data Augmentation
We present a discriminative nonparametric latent feature relational model
(LFRM) for link prediction to automatically infer the dimensionality of latent
features. Under the generic RegBayes (regularized Bayesian inference)
framework, we handily incorporate the prediction loss with probabilistic
inference of a Bayesian model; set distinct regularization parameters for
different types of links to handle the imbalance issue in real networks; and
unify the analysis of both the smooth logistic log-loss and the piecewise
linear hinge loss. For the nonconjugate posterior inference, we present a
simple Gibbs sampler via data augmentation, without making restricting
assumptions as done in variational methods. We further develop an approximate
sampler using stochastic gradient Langevin dynamics to handle large networks
with hundreds of thousands of entities and millions of links, orders of
magnitude larger than what existing LFRM models can process. Extensive studies
on various real networks show promising performance.Comment: Accepted by AAAI 201
How volatilities nonlocal in time affect the price dynamics in complex financial systems
What is the dominating mechanism of the price dynamics in financial systems
is of great interest to scientists. The problem whether and how volatilities
affect the price movement draws much attention. Although many efforts have been
made, it remains challenging. Physicists usually apply the concepts and methods
in statistical physics, such as temporal correlation functions, to study
financial dynamics. However, the usual volatility-return correlation function,
which is local in time, typically fluctuates around zero. Here we construct
dynamic observables nonlocal in time to explore the volatility-return
correlation, based on the empirical data of hundreds of individual stocks and
25 stock market indices in different countries. Strikingly, the correlation is
discovered to be non-zero, with an amplitude of a few percent and a duration of
over two weeks. This result provides compelling evidence that past volatilities
nonlocal in time affect future returns. Further, we introduce an agent-based
model with a novel mechanism, that is, the asymmetric trading preference in
volatile and stable markets, to understand the microscopic origin of the
volatility-return correlation nonlocal in time.Comment: 16 pages, 7 figure
- …