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Self-similar processes in collective risk theory

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  • Zbigniew Michna

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.

Suggested Citation

  • Zbigniew Michna, 1998. "Self-similar processes in collective risk theory," International Journal of Stochastic Analysis, Hindawi, vol. 11, pages 1-20, January.
    • Handle: RePEc:hin:jnijsa:373865
    DOI: 10.1155/S1048953398000367
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    Cited by:

    1. Bisewski, Krzysztof & DeĢ§bicki, Krzysztof & Kriukov, Nikolai, 2023. "Simultaneous ruin probability for multivariate Gaussian risk model," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 386-408.

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