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A new risk model is constructed, where the total number of claims
satisfies the geometric first-order integer-valued autoregressive process. Moreover, we
obtain the equation of the adjustment coefficient. We discuss the relationships among the
dependence on the number of claims in each period, the adjustment coefficient, and ruin
probability by numerical simulations. The results show that, with the increase of the
dependence on the number of claims in each period, the adjustment coefficient decrease and
ruin probability increase gradually.
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In this article, using the limit theory of martingales, we study the
moderate deviation for maximum likelihood estimator of unknown parameter in the stochastic
partial differential equation driven by additive fractional Brownian motion with Hurst
parameter , and the rate function can be calculated. Moreover, we apply our
main result to several examples.
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In this paper, we propose a joint mean-variance-correlation modeling
approach for longitudinal studies. By applying partial autocorrelations, we obtain an
unconstrained parametrization for the correlation matrix that automatically guarantees its
positive definiteness, and develop a regression approach to model the correlation matrix
of the longitudinal measurements by exploiting the parametrization. The proposed modeling
framework is parsimonious, interpretable, and flexible for analyzing longitudinal data. Real
data example and simulation support the effectiveness of the proposed approach.
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This article provides the readers with an introduction to the
spectral theory of ergodic one dimensional Schrodinger operators. The theorems
developed by the author are mainly discussed and their proofs are given in detail.
