Self-similar processes in collective risk theory. (1998)

• Record Type: Journal Article
• Authors: Michna, Zbigniew
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 11:Number 4(1998)
• Page Start: 429
• Page End: 448
• Publication Date: 1998
• Subjects: risk process -- long range dependence -- ruin probability -- self-similar process -- fractional Brownian motion -- exponential bound; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953398000367
• Languages: English
• ISSNs: 1048-9533

Abstract

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.