The paper deals with the renewal risk model. A precise large deviation result in the case of subexponential claim sizes is proved. As a special case, the example of Pareto distributed claim sizes and inter-occurrence times is investigated.

This paper deals with the asymptotic behavior for the tail probability of randomly weighted sums of subexponential random variables under a dependence structure, where the random weights and the corresponding summands are dependent.

In this paper, we consider the randomly weighted sum S2Θ=Θ1X1+Θ2X2, where the two primary random summands X1 and X2 are real-valued and dependent with long or dominatedly varying tails, and the random weights Θ1 and Θ2 are positive, with values in [a,b], 0a≤b∞, and arbitrarily...

We prove the consistency of a family of CUSUM-type estimators of the point of change in the mean of dependent observations and derive the rates of convergence. The result is valid under weak assumptions on the dependence structure.

In this paper, we study a general stochastic trend model and provide conditions on the partial sums which imply the convergence of the V/S statistic. These conditions generalize those in Giraitis et al. (J. Appl. Probab. 38 (2001) 1033) obtained in the case of deterministic trend model. As a...

Let {Sn:n≥0} be a random walk with negative drift and τ(x) be the first time when the random walk crosses a given level x≥0. This paper focuses on random walks with non-convolution equivalent increments. For this random walk, the uniform asymptotics of P(Sτ(x)−xy,τ(x)∞), as x→∞,...

This paper deals with some negatively dependent risk models with a constant interest rate, dominatedly-varying-tailed claims and a general premium process. We first establish two weak asymptotic equivalent formulae for the finite-time ruin probabilities. Furthermore, we obtain a uniform result...

Let F be a proper distribution on D=[0,[infinity]) or (-[infinity],[infinity]) and N be a non-negative integer-valued random variable with masses . Denote . The main result of this paper is that under some suitable conditions, G belongs to the convolution equivalent distribution class if and...