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 consider the long memory and leverage properties of a model for the conditional variance of an observable stationary sequence, where the conditional variance is the square of an inhomogeneous linear combination of past values of the observable sequence, with square summable weights. This...

The paper is concerned with the estimation of the long memory parameter in a conditionally heteroskedastic model proposed by Giraitis, Robinson and Surgailis (1999). We consider methods based on the partial sums of the squared observations which are similar in spirit to the classical R/S...

We consider the long memory and leverage properties of a model for the conditional variance of an observable stationary sequence, where the conditional variance is the square of an inhomogeneous linear combination of past values of the observable sequence, with square summable weights. This...