Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 4, Pages 429-448
doi:10.1155/S1048953398000367
Abstract
Collective risk theory is concerned with random fluctuations of the total
assets and the risk reserve of an insurance company. In this paper we consider self-similar, continuous processes with stationary increments for the
renewal model in risk theory. We construct a risk model which shows a
mechanism of long range dependence of claims. We approximate the risk
process by a self similar process with drift. The ruin probability within
finite time is estimated for fractional Brownian motion with drift. A
similar model is applicable in queueing systems, describing long range dependence in on/off processes and associated fluid models. The obtained results are useful in communication network models, as well as storage and
inventory models.