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In this paper, we introduce a class of stochastic age-dependent
population equations with Poisson jumps. Existence and uniqueness of energy solutions for
stochastic age-dependent population dynamic system are proved under local non-Lipschitz
condition in Hilbert space.
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We consider probabilistic meanings for some numerical characteristics of single birth processes. Some probabilities of events, such as extinction probability, returning probability, are represented in terms of these numerical characteristics. Two examples are also presented to illustrate the value of the results.
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Besides the claims data in the past, certain assumptions about
the distribution of claimsare required to derive the credibility
premium in the classical theory. In the paper, the credibility premium can be calculated
via the maximum entropy method if we know nothing about the distribution of claims . Furthermore, two corollaries are obtained under certain assumptions, that is, new claims have more weight than the old ones and the classical credibility
formula is a special case of the credibility premium derived in the present paper.
Finally, the simulation study is presented to illustrate that the credibility premium
in the present paper is better than other models if the mean square error is taken as
the evaluation criterion.
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This paper studies the price of convertible bonds with
counterparty credit risk in a reduced-form model. We suppose that the default intensity
process and the interest rate process follow the Vasicek model, and derive the price
expression of convertible bonds using the method of measure changes. Moreover, we make
some numerical analysis on the explicit formulae to demonstrate the sensitivity of a
convertible bond price to changes in the parameters of the model.
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Let be an array of rowwise
asymptotically almost negative associated (AANA, in short) random variables. The
complete convergence for weighted sums of arrays of rowwise AANA random variables
is established under some general moment conditions. The result obtained in the
paper generalizes and improves the corresponding one for negatively associated
random variables.
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Recently, big data, could computing and internet of things
provide some new information technologies for organization and management of complex
systems, and they have caused multifaceted changes on organization framework and
operations mechanism of enterprises. Based on this, we first construct a new stochastic
model for a big data driven large-scale bike-sharing system, which expresses the
important role played by big data, and describes the operations mechanism of the
large-scale bike-sharing system, and specifically, the rebalancing of bikes in various
stations in terms of trucks. Then, we present a mean-field limit theory, which is
applied to analyzing the big data driven large-scale bike-sharing system, including
establishing a time-inhomogeneous queueing system by means of the mean field theory,
and setting up the mean-field equations through the time-inhomogeneous queueing system;
providing an empirical measure process by means of a nonlinear birth-death process,
giving algorithms for computing the fixed point in terms of a segmented structural
birth-death processes, and computing the average number of bikes in each station; and
providing numerical examples to analyze how the steady average number of bikes in each
station depends on some key parameters of the bike-sharing system. Using these results,
this paper analyzes physical effect of big data on performance of the large-scale
bike-sharing. Therefore, this paper gives a promising research direction of stochastic
model in the study of large-scale bike-sharing systems.
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The mean residual life (MRL) function plays a very important
role in the area of reliability engineering, survival analysis, and many other fields.
In this paper, we introduce and study a new stochastic order which gives stochastic
comparison for mean residual life of strictly increasing concave function of two
random variables. We show that this new stochastic order lies between the hazard
rate and mean residual life orders. The preservation properties under mixtures are
presented here. Finally, we give some applications of this new order in reliability
theory.
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This paper considers a dividend strategy with investment in
Omega model. If at a potential dividend-payment time the surplus is above , part
of the excess are paid as dividends directly, the other part are used as dynamic
investment capital, at a particular time, the sum of profits and investment capital
will be paid as another dividend. Under this dividend policy, we get the optimal
dividend strategy and the optimal portfolio policy.
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In this paper, the multivariate linear statistical method is
applied to research the undergraduate grades of students from the school of mathematics
in Hefei University of Technology, and explore the impact on the later achievement by
the early stage of achievement from all undergraduate courses. First, we get the main
components from the previous courses by principal component analysis, then construct a
linear regression model between the later achievement and main components by the stepwise
regression method. Next, a linear regression model between the later achievement and the
early stage of achievement from all undergraduate courses is constructed by Adaptive-Lasso
method. Finally, comparative analysis is performed for the result of the above models. The
research shows that the principal component regression model based on the Adaptive-Lasso
method can well fit the later achievement, and give a reasonable explanation for the later
academic performance.
