Self-similar processes in collective risk theory

Zbigniew Michna

International Journal of Stochastic Analysis, 1998, vol. 11, 1-20

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.

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:373865

DOI: 10.1155/S1048953398000367

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