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Consider a risk model in which the claims follow a non stationary arrival process that satisfies a large deviation principle. Supposing that the claim sizes form a sequence of i.i.d. random variables with subexponential tail, precise large deviations for the aggregate claims are obtained, by allowing the claim-sizes and claim inter-arrival (waiting) times to be arbitrarily dependent. [ABSTRACT FROM AUTHOR]

Consider a risk model with consistently-varying-tailed claim sizes following a Hawkes-type arrival process. By allowing that the extended negatively dependent claim sizes and the claim inter-arrival (waiting) times are arbitrarily dependent, moderate deviation results for the aggregate amount of claims are obtained. [ABSTRACT FROM AUTHOR]

Consider the AR(1) model, X t = θ X t − 1 + u t , where { u t ; t ≥ 1 } is a sequence of long memory processes with possibly infinite variance. In this paper, we propose to use a residual-based m-out-of-n bootstrap procedure to approximate the distribution of a least-squares estimator for the autoregressive parameter when this parameter is equal to unity, and its asymptotic validity is also proved. [ABSTRACT FROM AUTHOR]

Consider a multidimensional risk model, in which an insurer simultaneously confronts m (m ≥ 2) types of claims sharing a common non-stationary and non-renewal arrival process. Assuming that the claims arrival process satisfies a large deviation principle and the claim-size distributions are heavy-tailed, asymptotic estimates for two common types of ruin probabilities for this multidimensional risk model are obtained. As applications, we give two examples of the non-stationary point process: a Hawkes process and a Cox process with shot noise intensity, and asymptotic ruin probabilities are obtained for these two examples. [ABSTRACT FROM AUTHOR]

We consider the nearly nonstationary autoregressive model yt = qnyt−1+ut, where qn = 1−c/n, c is a fixed constant, and {ut, t ≽ 1} is a sequence of innovations belonging to the domain of attraction of a stable distribution with index 0 < α < 2. We construct a composite quantile regression estimator for the autoregressive coefficient and establish the asymptotic distribution of this estimator under some mild conditions. [ABSTRACT FROM AUTHOR]

In this paper, we consider a risk model with heavy-tailed claims and Brownian perturbation. Assuming that the distribution function of claim-size is subexponential, and the arrival process of claims is a non stationary process satisfying the principle of large deviation, the asymptotic formula for the ruin probability of this risk model at random time is obtained. [ABSTRACT FROM AUTHOR]

Consider a particular bidimensional risk model, in which two insurance companies divide between them in different proportions both the premium income and the aggregate claims. In practice, it can be interpreted as an insurer–reinsurer scenario, where the reinsurer takes over a proportion of the insurer's losses. Under the assumption that the claim sizes and inter-arrival times form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure, an asymptotic expression for the ruin probability of this bidimensional risk model with constant interest rates is established. [ABSTRACT FROM AUTHOR]

This article studies a bidimensional risk model, in which an insurer simultaneously confronts two kinds of claims sharing a common non-stationary arrival process. Assuming that the arrival process satisfies a large deviation principle and the claim-size distributions are heavy tailed, an asymptotic formula for the corresponding ruin probability of this bidimensional risk model is obtained. [ABSTRACT FROM AUTHOR]

Consider a two-dimensional risk model, in which two insurance companies divide between them the claims in some specified proportions. Suppose that the claim sizes and inter-arrival times form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure, and the surpluses of the two companies are invested into portfolios whose returns follow two different geometric Lévy processes. When the claim-size distribution is extended-regularly-varying tailed, asymptotic expressions for the ruin probability of this two-dimensional risk model are exhibited. Some numerical results are also presented to illustrate the accuracy of our asymptotic formulae. [ABSTRACT FROM AUTHOR]

Consider a risk model with claims of heavy tails for non stationary arrival processes that satisfy a large-deviation principle. Assume that the claim sizes and interarrival times form a sequence of random pairs, with each pair obeying a dependence structure via the conditional distribution of the interarrival time given the subsequent claim size being large, and then a precise large-deviation formula of the aggregate amount of claims is obtained. [ABSTRACT FROM PUBLISHER]

In this article, we consider a non standard renewal risk model, in which pairs of claim sizes and its corresponding inter-arrival times are identically distributed, and each pair obeys a dependence structure. By assuming that the claim sizes form a sequence of extended negatively dependent random variables with consistently varying tails, moderate deviations for the aggregate amount of dependent claims are obtained. [ABSTRACT FROM PUBLISHER]

Consider a continuous-time risk model with two correlated classes of insurance business and a constant force of interest. Suppose that the correlation comes from a common shock, and that the claim sizes and inter-arrival times correspondingly form a sequence of random pairs, with each pair obeying a dependence structure. By assuming that the claim sizes are heavy tailed, a uniform tail asymptotic formula for the sum of the two correlated classes of discounted aggregate claims is obtained. [ABSTRACT FROM AUTHOR]

Consider a nonstandard renewal risk model, in which every main claim induces a delayed by-claim. Suppose that the surplus is invested to a portfolio of one risk-free asset and one risky asset, and the main claim sizes with by-claim sizes form a sequence of pairwise quasi-asymptotically independent random variables with dominatedly varying tails. Under this setting, asymptotic behavior of the ruin probability of this renewal risk model is investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity. Some numerical results are also presented to illustrate the accuracy of our asymptotic formulae. [ABSTRACT FROM AUTHOR]

In this paper we study the joint ruin problem for two insurance companies that divide between them the losses in positive proportions δ 1 and δ 2 (modeling an insurance and a re-insurance company). Assume that the surplus process of i -th ( i = 1 , 2 ) company U i has the form of d U i ( t ) = U i ( t − ) d R i ( t ) − δ i d P ( t ) , t > 0 , with U i ( 0 ) = x i > 0 , and P and R i two Lévy processes representing, respectively, a loss process and a stochastic return process. Supposing that the loss process P has a Lévy measure of consistent variation and the Laplace exponent of R i ( i = 1 , 2 ) satisfies some conditions, an asymptotic estimate for this joint ruin problem is established. [ABSTRACT FROM AUTHOR]

In this article, the unit root test for the AR(1) model is discussed, under the condition that the innovations of the model are in the domain of attraction of the normal law with possibly infinite variances. By using residual bootstrap with sample sizem

Consider a random coefficient AR(1) model, X t = ( ρ n + ϕ n ) X t − 1 + u t , where { ρ n , n ≥ 1 } is a sequence of real numbers, { ϕ n , n ≥ 1 } is a sequence of random variables, and the innovations of the model form a sequence of i.i.d. random variables belonging to the domain of attraction of the normal law. By imposing some weaker conditions, the conditional least squares estimator of the autoregressive coefficient ρ n is achieved, and shown to be asymptotically normal by allowing the second moment of the innovation to be possibly infinite. [ABSTRACT FROM AUTHOR]

Consider a continuous-time risk model with two correlated classes of insurance business and risky investments whose price processes are geometric Lévy processes. By assuming that the correlation comes from a common shock, and the claim sizes are heavy-tailed and pairwise quasi-asymptotically independent, we investigate the tail behavior of the sum of the stochastic present values of the two correlated classes, and a uniform asymptotic formula is obtained. [ABSTRACT FROM AUTHOR]

Let {Xk;k≥1} be a long memory process defined bywhere {ϵi;−∞

Abstract: Under the polynomial decay rates and finite second moment, a strong approximation theorem for partial sums of linear positive quadrant dependent Gaussian sequences is derived. As applications, the law of the iterated logarithm, the Chung-type law of the iterated logarithm and the almost sure central limit theorem are obtained with minimal conditions. [Copyright &y& Elsevier]

Let { X, X; n≧1} be a sequence of B-valued i.i.d. random variables. Denote $X_{{n}}^{(r)}=X_{{m}}$ if ∥ X∥ is the r-th maximum of {∥ X∥; k≦ n}, and let ${}^{(r)}S_{{n}}=S_{{n}}-(X_{{n}}^{(1)}+\cdots+X_{{n}}^{(r)})$ be the trimmed sums, where $S_{{n}}=\sum_{ k=1}^{n}X_{{k}}$. Given a sequence of positive constants { h( n), n≧1}, which is monotonically approaching infinity and not asymptotically equivalent to loglog n, a limit result for $^{(r)}S_{{n}}/\sqrt{2nh(n)}$ is derived. [ABSTRACT FROM AUTHOR]

Abstract: Let be a strictly stationary associated sequence of random variables taking values in a real separable Hilbert space, and be a sequence of bounded linear operators. For a linear process , the precise probability and moment convergence rates of in some limit theorems are discussed. [Copyright &y& Elsevier]

Functional regression functions, with explanatory variables taking values in some abstract function space, have been studied extensively. In this article, we aim to investigate the multivariate functional regression function, and propose a nonparametric estimator for the multivariate case. By applying some properties of U-statistics, some asymptotic distributions of such estimator are obtained under different cases. [ABSTRACT FROM AUTHOR]

Abstract: Let be a sequence of independent and identically distributed random variables, taking values in a separable Banach space B with topological dual . Considering the geometrically weighted series for , motivated by Einmahl and Li (2005, 2008), a general law of the iterated logarithm for is established. [Copyright &y& Elsevier]

Abstract: Let be a -statistic based on a symmetric kernel and -mixing samples . Under some suitable conditions, the weak convergence of the self-normalized -statistics is obtained, which extends a previous result for independent cases. [Copyright &y& Elsevier]

Let be a U-statistic based on a kernel function h(x 1, x 2) and independent and identically distributed samples {X n ; n ≥ 1}. The author obtained a weak invariance principle and a strong functional limit theorem for the products of when may be infinite. Moreover, the author also applies the results to the sample variance and the Gini's mean difference, and obtain the limiting properties of their products. [ABSTRACT FROM AUTHOR]

Abstract: For a sequence of φ-mixing -valued random vectors , based on the Berkes–Philipp coupling construction and the blocking method with growing blocks, a general strong approximation theorem is derived without second absolute moment, which extends previous result for independent cases. [Copyright &y& Elsevier]

Let { X, X; n≧0} be a sequence of identically distributed ψ-mixing dependent random variables taking values in a type 2 Banach space B with topological dual B. Considering the geometrically weighted series $\xi(\beta)= \sum_{n=0}^{\infty}\beta^{n}X_{n}$ for 0< β<1, a general law of the iterated logarithm for ξ( β) is obtained without second moment. [ABSTRACT FROM AUTHOR]

Let {Xk; k ≥ 1} be a linear process defined by [image omitted] where {εi; - ∞