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In this paper, we study the pricing of
defaultable bonds and credit default swaps with counterparty risk
using a contagion model. We present a contagion model of correlated
defaults in a reduced model. The model assumes the intensities of
default processes depend on the stochastic interest rate process
driven by a stochastic differential equation and the default process
of a counterparty. These are extensions of the models in Jarrow and
Yu (2001) and Hao and Ye (2011). Moreover, we derive the explicit
formulae for the pricing of defaultable bonds and credit default
swap with counterparty risk using the properties of stochastic
exponentials and make some numerical analysis on the explicit
formulae.
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The supermarket model is a dynamic randomized
load balancing scheme for real-time dynamic control of large-scale
parallel queuing network. It has many important practical applications
in, for example, computer networks, cloud computing, manufacturing systems
and transportation networks. In this paper, for the supermarket models
we consider some important issues, such as, real-time dynamic control
modes; efficiency comparison; mean-field black hole; Markov changing
environment; stability; fixed point; system performance analysis.
At the same time, we also study these important issues through some
numerical examples, include performance comparison, and efficiency
analysis for advantages and disadvantages among the supermarket
models with either customers joining the shortest queue, or customers
joining any queue randomly, or customers joining the longest queue.
Further, we consider a more general supermarket model under an Markov
changing environment, and provide performance evaluation for the
supermarket model under an Markov changing environment.
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In this paper, we focus on the estimation
for the marginal semiparametric partially linear models with longitudinal
data when some covariates are measured with additive errors. We first
approximate the nonparametric part of the model based on the B-splines
and a new bias-corrected estimation procedure is proposed based on the
quadratic inference functions (QIF). Under some regularity conditions,
we show that the QIF estimator is consistent and asymptotically normal.
Extensive simulation studies and an application are conducted to examine
the finite sample performance of the proposed estimation procedure.
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This paper studies significant differences
in functional connectivity between schizophrenia patients and healthy
controls by different methods. Firstly, three different brain functional
networks are constructed by Pearson correlation coefficient, partial
correlation coefficient and wavelet correlation coefficient, and then
the paper uses risk difference to find out those significant differences.
Finally, a comparative analysis is made. The result shows that common
and abnormal connectivity exists in different networks where functional
connectivity between the precuneus and posterior cingulate cortex weakens
significantly among schizophrenia patients compared with controls. And
more notably, the sign of some statistic appears in some significant
functional connectivity is completely contrary. That is to say, as
opposed to controls this functional connectivity in patients is both
strengthened and weakened simultaneously. It shows that statistical
test makes the results more persuasive as searching for abnormal
functional connectivity in brain networks in terms of statistics.
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In this article, we propose an efficient
method to identify an informative correlation structure for
longitudinal data based on varying-coefficient models and the
proposed approach yields a more efficient estimator for the
coefficient curves. Simulation and real data example show that the
proposed method has efficiency in selecting and estimating the true
correlation structure in finite samples and the estimation
efficiency of the coefficient curves is improved by using the
selected correlation structure in the estimation procedure.
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The author discusses the complete moment
convergence for weighted sums of arrays of -mixing random
variables. The obtained results in this paper improve the
corresponding ones of Qiu (2011).
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Binomial model is one of widely used models,
and its parameters have a great influence on option pricing. In this
paper, a new parameter estimation is given for binomial model, which
overcomes the fault of usual methods to estimate parameters of
binomial models, especially, eliminate the influence of subjective
probability.
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Growth curve model is a general multivariable
linear model. It plays an important role in modern statistics. In this
paper, firstly, we define the penalized least squares for growth curve
model, after transforming it by the Potthoff-Roy transformation. By
using adaptive LASSO we can get corresponding estimation, as well as
achieve the variable selection. Then, the penalized least squares
estimation of the growth curve model is presented with a unified expression
of approximate estimation. In addition, we discuss the properties of
the penalized least squares estimations of the growth curve model,
which is transformed by Potthoff-Roy transformation, and the properties,
which are Oracle properties, are proved in this paper. By using the
criteria to measure estimation and variable selection, we compare
several penalized least squares estimations and the effect of variable
selection of different penalty functions. The result shows that the
adaptive LASSO performs better in parameter estimation and variable
selection. Besides, we compare different transformations. Results
indicate that Potthoff-Roy transformation performs better than matrix
stacking transformation when considering variable selection and
parameter estimation comprehensively.
