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In this note, we consider a class of
backward stochastic differential equations with non-uniformly
Lipschitz coefficients. We prove the existence and uniqueness of the
solutions with 1<p
.
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In this paper we use stochastic optimal
control theory to investigate a dynamic portfolio selection problem
with liability process, in which the liability process is assumed to
be a geometric Brownian motion and completely correlated with stock
prices. We apply dynamic programming principle to obtain
Hamilton-Jacobi-Bellman (HJB) equations for the value function and
systematically study the optimal investment strategies for power
utility, exponential utility and logarithm utility. Firstly, the
explicit expressions of the optimal portfolios for power utility and
exponential utility are obtained by applying variable change
technique to solve corresponding HJB equations. Secondly, we apply
Legendre transform and dual approach to derive the optimal portfolio
for logarithm utility. Finally, numerical examples are given to
illustrate the results obtained and analyze the effects of the
market parameters on the optimal portfolios.
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In this paper, the authors discuss the moment
complete convergence for weighted sums of -mixing random
variables, and obtains the sufficient condition for moment complete
convergence of -mixing sequence under some mixing rate
condition, which generalize the result of moment complete
convergence for weighted sums of i.i.d. random variables to
-mixing random variables.
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Under the condition of h-integrability
with respect to an array of weights, the moment convergence for
weighted sums of pairwise negative quadrant dependent random
variables is studied. The authors obtain a new result, and solve the
open problem in Sung et al. ,(2008) and improve the corresponding
theorem of Cabrera and Volodin (2005).
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This paper studies non-parametric kernel
estimates of the time-dependent diffusion equation based on the
observations of discrete samples. We construct local kernel
estimation of the time-dependent diffusion coefficient using
"sectional" method. Furthermore we proved the strong consistency
of the estimator.
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Stationary long memory process has been
widely studied in the literature. In this article, we considered the
locally stationary long memory process with time-varying memory
parameter. A new wavelet-based algorithm was developed using
log-linear relationship between the wavelet coefficient variance and
the scaling parameter. The consistency and the finite sample
behavior of the estimator have also been studied, which provide a
good reference for the practitioner and researchers. The new
algorithm has also been applied to the YEN/USD exchange rate series,
which leads to some interesting results.
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In some biological experiments, it is
quite common that laboratory subjects may be different in their
patterns of susceptibility to a treatment. We need to determine the
different patterns of susceptibility. In this paper we model the
number of susceptibility's patterns and the parameters jointly, and
base inference about these quantities on their posterior
probabilities, making use of reversible jump Markov chain Monte
Carlo methods that are capable of jumping between the parameter
subspaces corresponding to different numbers of components in the
mixture. For convenience, we always assume different patterns of
susceptibility have common variances. The paper apply the
methodology to the analysis of univariate normal mixtures with
different variances. The practical significance of the proposed
method is illustrated with a dose-response data set.
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The robustness of regression coefficient
estimator is a hot topic in regression analysis all the while. Since
the response observations are not independent, it is extraordinarily
difficult to study this problem for random effects growth curve
models, especially when the design matrix is non-full of rank. The
paper not only gives the necessary and sufficient conditions under
which the generalized least square estimate is identical to the the
best linear unbiased estimate when error covariance matrix is an
arbitrary positive definite matrix, but also obtains a concise
condition under which the generalized least square estimate is
identical to the maximum likelihood estimate when the design matrix
is full or non-full of rank respectively. In addition, by using of
the obtained results, we get some corollaries for the the
generalized least square estimate be equal to the maximum likelihood
estimate under several common error covariance matrix assumptions.
Illustrative examples for the case that the design matrix is full or
non-full of rank are also given.
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In this paper, we consider the compound
Poisson surplus model with interest, liquid reserves and a constant
dividend barrier. When the surplus of an insurer is below a fixed
level, the surplus is kept as liquid reserves, which does not earn
interest. When the surplus attains the level, the surplus will
receive interest at a constant rate. When the surplus hits another
fixed higher lever, the excess of the surplus over this higher level
will be distributed to the shareholders as dividends. We derive a
system of integro-differential equations for the Gerber-Shiu
discounted penalty function and obtain the solutions to these
integro-differential equations. In the case where the claim sizes
are exponential distributed, we get the exact solutions of zero
discounted Gerber-Shiu function. We also get the
integro-differential equation for the expectation of the discounted
dividends until ruin which is the key to discuss the optimal
dividend barrier. And we give the exact solution in the special case
with exponential claim sizes.
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Zero-inflated Poisson (ZIP) regression
model is a popular tool for analyzing count data with excess zeros.
In this paper, a flexible hierarchical ZIP regression model is
proposed to handle with such data with cluster and Bayesian approach
is develop. A Gibbs sampler is employed to produce the Bayesian
estimate, a goodness-of-fit and a Bayesian information criterion
(BIC) are used for model comparison and selection. Finally, an
application of data from a ship damage incident study illustrates
the proposed method.
