373 research outputs found
A bivariate risk model with mutual deficit coverage
We consider a bivariate Cramer-Lundberg-type risk reserve process with the
special feature that each insurance company agrees to cover the deficit of the
other. It is assumed that the capital transfers between the companies are
instantaneous and incur a certain proportional cost, and that ruin occurs when
neither company can cover the deficit of the other. We study the survival
probability as a function of initial capitals and express its bivariate
transform through two univariate boundary transforms, where one of the initial
capitals is fixed at 0. We identify these boundary transforms in the case when
claims arriving at each company form two independent processes. The expressions
are in terms of Wiener-Hopf factors associated to two auxiliary compound
Poisson processes. The case of non-mutual (reinsurance) agreement is also
considered
Useful martingales for stochastic storage processes with L\'{e}vy-type input
In this paper we generalize the martingale of Kella and Whitt to the setting
of L\'{e}vy-type processes and show that the (local) martingales obtained are
in fact square integrable martingales which upon dividing by the time index
converge to zero a.s. and in . The reflected L\'{e}vy-type process is
considered as an example.Comment: 15 pages. arXiv admin note: substantial text overlap with
arXiv:1112.475
Networks of Server Queues with Shot-Noise-Driven Arrival Intensities
We study infinite-server queues in which the arrival process is a Cox process
(or doubly stochastic Poisson process), of which the arrival rate is given by
shot noise. A shot-noise rate emerges as a natural model, if the arrival rate
tends to display sudden increases (or: shots) at random epochs, after which the
rate is inclined to revert to lower values. Exponential decay of the shot noise
is assumed, so that the queueing systems are amenable for analysis. In
particular, we perform transient analysis on the number of customers in the
queue jointly with the value of the driving shot-noise process. Additionally,
we derive heavy-traffic asymptotics for the number of customers in the system
by using a linear scaling of the shot intensity. First we focus on a one
dimensional setting in which there is a single infinite-server queue, which we
then extend to a network setting
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