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Review of statistical actuarial risk modelling. (English) Zbl 1426.62308

Summary: In this paper, we review some results for insurance risk theory. We first introduce a variety of the insurance risk models proposed thus far. Then, we show that the expected discounted penalty function (the so-called Gerber-Shiu function) can describe some risk indicators. Next, the dividend problem is discussed; more precisely, the (approximated) optimal dividend barrier is derived and other extended dividend strategies introduced. In addition, some modified models depending on reinsurance or tax are introduced. Finally, we discuss the statistical estimation of the ruin probability and the Gerber-Shiu function.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62-02 Research exposition (monographs, survey articles) pertaining to statistics
91G05 Actuarial mathematics
91B05 Risk models (general)
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