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The strong stability of linear forms had found many applications in the science and technology. In this
paper, we investigate the strong stability of linear forms for mixing sequence. By using the termination, Borel-Cantelli
lemma and properties of mixing sequence, the sufficient
condition of the strong stability of linear forms for mixing
sequence is given. Stability of other linear forms in mixing
sequence are given at the same time
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The convergence property of the solution
for finite horizon reflected backward stochastic equations was
obtained in this paper. The same conclusion was also proved with
infinite horizon.
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A reversible Markov process which permits coagulation
and fragmentation reactions is considered. We analyze the covariance
of small, medium and large molecules in three distinct stages
(subcritical, critical and supercritical stages) of polymerization
and prove that long term correlation only exists in the critical
stage.
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Credit risk theory has become one of the
cutting edges in modern finance over the past few years. We
investigate into one of the important issues amongst portfolio's
credit risk: Copula's applications in correlated default. We
discover the relationship amongst Copula and other tools for the
correlated default, such as structural models and reduced form
models. Additionally, different from Lando (1998), we present
another method and proof for the calculation of default probability
of the single firm.
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Absolute ruin, expected discounted penalty
function, integro-differential equation, probability of recovery.
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In this paper, a new model is constructed
by taking uncertain environment into consideration for the
bankruptcy risk problems in term life insurance, where the mortality
rate is regarded as an interval parameter and the net insurance
policy is a random parameter. Formula for computing the interval
probability of bankruptcy is obtained, an approximation method owing
to Poisson distribution is studied. Since some important aspects
have been taken into consideration in the new formulation, such as
the accumulating interest of initial reserve, the entry of new
customers at any time, the design of new grouping fashion and the
uncertain environment, the result obtained in this paper is more
practical than the existing models.
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Mean and covariance structure model is
widely applied in behavioral, educational, medical, social and
psychological research. The classic maximum likelihood estimate is
vulnerable to outliers and distributional deviation. In this paper,
robust estimate based on minimizing the objective function is
proposed, and M-ratio test based on the robust deviance is suggested
to assess the model fit. Empirical results are illustrated by a real
example.
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By using limit distribution of Markov
skeleton processes, the article studies homogeneous denumerable
semi-Markov processes and obtains their limit distribution. When the
distribution of renewal interval is non-lattice, the result obtained
in this paper is consistent with that in ,but the
approaches this article used are Markov skeleton processes
approaches which differ from .Furthermore, when the
distribution of renewal interval is lattice, this paper gives the
result, whereas didn't study this case. Finally, this
article generalizes the limit distribution of homogeneous
denumerable semi-Markov processes, and illustrates the result
through one example.
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In this paper, we primarily study the
strong law of large numbers and the law of large numbers of some
special functions for Markov chains in unidirectional infinitely
Markovian environments, and give some sufficient conditions on the
jointly Markov chains and the sample function of the jointly Markov
chains.
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This paper extends Hull-White interest
rate model to cover cross-currency case. In the extended model we
discuss valuation of cross-currency Bermudan swaptions. Since the
closed-form pricing formula is hard to obtain, we apply the Least
Squared Monte-Carlo approach to find the optimal exercising time.
Some numerical results with different parameters are presented.
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In this article, we examine the daily
structure of stock price indices in the major stock markets in
Asia-Pacific area using fractional integrated techniques. According
to the long memory characteristics of the data, a particular version
of Robinson's (1994) test is proposed for testing unit roots and
non-stationarity in the financial data. The results show that the
long memory behavior of the stock price indices in this region is
different but quite similar.
