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We obtain some sufficient conditions of
complete convergence for Weighted Sums of Arrays of B-Valued Random
Elements which are stochastically dominated by a random variable.
Some results in 9 and 6 are extended
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A mixed diffusion process involving various
sources of jumps is introduced to characterize both the price of
underlying asset and the ratio of firm's assets to liabilities.
Continuous component is modeled as geometric Brownian motion to
describe their ``normal'' revolution, and discontinuous component is
modeled as jumps with several Poisson arrival processes in
conjunction with corresponding random jump size to characterize
their sudden increase or drop in a surprising manner
instantaneously. This may be due in part to the impact of rare
events and new information, such as technological innovation,
regulatory effects, catastrophic rare events and so on $\ldots$
These jumps are assumed independent of each other, with each type
having a log-normally distributed jump size, we also supposed that
all jumps risk is diversifiable and hence not priced in equilibrium.
By applying It\^{o} lemma and equivalent martingale measure
transformation within the framework of our model, we derived a
closed form of analytic solution for vulnerable European option, and
therefore generalized classical formula for vulnerable European
option with jump and quantified the works by Zhou\,(2001) and
Lobo\,(1999).
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Item Response Theory (IRT) model is a dramatically
important model in educational and psychological measurement. There
are two kinds of parameters in the model --- item parameters and
ability parameters. Nowadays, a commonly used method for estimating
item parameters of IRT model is given by Woodruff and Hanson (1997).
They treated the ability parameter $\theta$ as missing and applied
EM Algorithm for finite mixture to estimate item parameters under
the condition that the examinees' responses are complete. Here, we
extend the Woodruff's method to deal with incomplete response data.
That is, we keep the incomplete response cases and regard missing
response data as ``missing'' like $\theta$ and then apply EM
Algorithm. In our simulation study, we compare the relative
performance of the missing data treatment method of us with that of
the software BILOG-MG under different sample size and missing ratio.
The simulation results show that our new method can obtain better
estimation than BILOG-MG in most cases.
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In this paper, we discuss a renewal risk process
(Sparre Andersen risk model) perturbed by diffusion in which the
claim inter-arrival times are generalized Erlang$(n)$ distributed.
The approach used is similar to that of Albrecher, et al.\,(2005),
decomposing a generalized Erlang$(n)$ random variable into an
independent sum of $n$ exponential random variables.
Integro-differential equations with certain boundary conditions for
the distribution of the maximum surplus before ruin are obtained.
The special case where the claim size distribution is a $K_m$
distribution is considered.
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In this paper, under some mild conditions,
precise large deviations for partial sums of negatively associated
random arrays in multi-risk models are investigated. The obtained
results extend some known ones, and we find out the asymptotic
behavior of precise large deviations is also insensitive to
negatively associated structures in multi-risk models.}
\newcommand{\fundinfo}{This work was supported by the National Natural
Science Foundation (10771070), Talents Youth Fund of Anhui Province
Universities (2011SQRL012ZD) and the 211 Project of Anhui University
(2009QN020B)
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Under the hypothesis of normal distribution,
the change-point problems have four cases according to mean and
variance changing. In this paper, we look upon the threshold
nonlinearity test of TAR models as a change-point problem, which has
a change-mean and constant-variance. We adopt reversible-jump Markov
chain Monte Carlo (RJMCMC) methods to calculate the posterior
probabilities of two competitive models, namely AR and TAR models.
Posterior evidence favoring the TAR model indicates threshold
nonlinearity. Simulation experiments demonstrate that our method
works very well in distinguishing AR and TAR models.
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Under condition that the sample size of
prior period is not always equal to the current's, the sample
rotation model is established. As a result, the optimal sample size
and rotation rate based on the given cost of sample survey, are
provided. Finally, three special cases are analyzed where the third
is the corresponding conclusions in literatures \cite{1,2}.
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In bisexual Galton-Watson branching process
with independent and identically distributed random environments, it
is shown that under certain conditions there exists
$0<\alpha<+\infty$ and $0<c<+\infty$ such that the extinction
probability starting with $k$ individuals is bounded above by
$ck^{-\alpha}$ for sufficiently large $k$.
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A market model with inner information is
constructed. The problem of quadratic hedging for investors with
inner information is introduced and solved. First the dynamic of
risky assets in the market with inner information is deduced using
the initial enlarge filtration method. Second by It\^{o} formula and
the decomposition of Galtchouk-Kunita-Watanabe the explicit optimal
strategy is given
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In terms of the generalized resolvent
equations this paper proves that a special potential term belongs to
the domain of the perturbed Dirichlet form, and gives two switching
identities directly using the perturbation of Dirichlet form.
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In classical regression credibility models
suggested by Hachemeister (1975), the risks are assumed to be
mutually independent. In this paper, we introduce a dependence
between risks induced by common effects and developed a credibility
regression model with dependence and the credibility predictors of
future claims and the estimators of risk parameters are derived
under this model. The results show that the credibility estimators
remain the weighted sums of individual and collective premium.
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In the paper, the results for linear
models with linear restrictions are partially extended to
linear mixed models for longitudinal data with general linear
restrictions. At the same time, regularity conditions in Li (2010)
were removed and the small sample properties of estimates are
investigated.
