This paper considers optimal designs based
on A-, Ds-, I- and D-optimality criteria for bivariate random
coefficient regression models. It is shown that the search of
optimal designs could be confined at extreme settings of the design
region and optimal approximate designs are obtained in the paper.

The future lifetimes of involved insured
persons in the multiple-life model are always assumed to be
independent in almost all actuarial textbooks. In this paper we
consider the two-life model and assume that the future lifetimes are
positively dependent. We use PQD (positively quadrant dependent) to
describe such dependence, and give a easy method to construct the
joint-life status life table.

In this paper we will discuss the inf-convolution
problems in the framework of multi-dimensional G-distributed
expectation, and we present the relationship between inf-convolution
of multi-dimensional G-distributed expectations and the
inf-convolution of drivers G. Moreover, we also study the continuity
and dynamical properties of this problem.

For a reduced form model of credit risk,
we use Cox process whose intensity process is a subordinator process
to define the default time of the company. We derive closed forms of
the distribution of the company's default time. We also derive the
fair price of the defaultable zero coupon bond and the credit spread
of the credit default swaps.

In this paper, we consider a discrete
time risk process with random interest force. With the assumption
that the interest rate process behaves as a Markov chain, we obtain
the recursive equations and integral equations for finite and
ultimate ruin probabilities, and Lundberg inequalities for the
ultimate ruin probabilities are also provided.

Letbe a sequence
of i.i.d. Gaussian random variables with zero mean and finite
variance, and set ,
.
In this paper, we prove that there exists positive constants  and ,
for small enough $\epsilon>0$, it follows that
, it follows that
.

For the analysis of partial linear model
with longitudinal data, the general procedure is to fit the
nonparametric part with kernel or spline estimation, followed by
generalized linear model estimating frame. In this paper, we fit the
nonparametric part with P-spline, and estimate the parametrical and
nonparametric part with different Generalized method of moments
estimation for different moment conditions, implemented by the proof
of the asymptotical properties for the estimator, which is also been
proved by simulation and illustrative example, from which we can
also find out that different penalized general method of moments
estimations for different moment conditions perform more
efficiently.

This paper is concerned with a portfolio
selection problem with stochastic interest rates and assumes that
interest rate is driven by the Ho-Lee model and the Vasicek model
respectively. We apply dynamic programming principle to derive the
HJB equation and use Legendre transform to obtain the dual one.
Quadratic utility function is taken for our analysis. The
closed-form solutions to the optimal investment strategy are derived
by applying variable change technique.

In this paper, we consider an extension of
semiparametric linear mixed-effect model to a class of longitudinal
data or clustered data with zero-inflation and propose a novel
semiparametric mixed model. Based on the maximum penalized
likelihood estimation and EM algorithm, we give a method for our
proposed model which may estimate both of the parameters and
nonparameters simultaneously. In the method, we use GCV to choose
the smoothing parameter.Finally, we study a simulation analysis and
one real data set to illustrate the proposed method.

We consider partially linear models in which
the linear covariate contains measurement errors, but instead an
observed surrogate that is linearly related to the unobserved
covariate. Moreover, the dimension of unobserved covariate diverges
with the sample size. We propose an estimation procedure and
establish the consistency and asymptotic normality property of
estimate. The rate of the divergent dimension is also investigated.
A simulation study and a real data are carried out to illustrate the
usefulness of the proposed method.