In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary...

We consider a Lévy process reflected in barriers at 0 and K  0. The loss rate is the mean of the local time at K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive...

We consider a Lévy process reflected in barriers at 0 and K  0. The loss rate is the mean of the local time at K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive...

This paper deals with estimating small tail probabilities of thesteady-state waiting time in a GI/GI/1 queue withheavy-tailed (subexponential) service times. The problem ofestimating infinite horizon ruin probabilities in insurancerisk processes with heavy-tailed claims can be transformed into...

This paper deals with estimating small tail probabilities of thesteady-state waiting time in a GI/GI/1 queue withheavy-tailed (subexponential) service times. The problem ofestimating infinite horizon ruin probabilities in insurancerisk processes with heavy-tailed claims can be transformed into...

This paper deals with estimating small tail probabilities of the steady-state waiting time in a GI/GI/1 queue with heavy-tailed (subexponential) service times. The problem of estimating infinite horizon ruin probabilities in insurance risk processes with heavy-tailed claims can be transformed...

This paper deals with estimating small tail probabilities of thesteady-state waiting time in a GI/GI/1 queue withheavy-tailed (subexponential) service times. The problem ofestimating infinite horizon ruin probabilities in insurancerisk processes with heavy-tailed claims can be transformed into...

Let fX;Xi; i = 1; 2; :::g denote independent positive random variables having a common distribution function F(x) and, independent of X, let N denote an integer valued random variable. Using S(0) = 0 and S(n) = S(n ?? 1) + Xn, the random sum S(N) has distribution function G(x) = 1Xi=0 P(N =...