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A survey of some recent results on risk theory. (English) Zbl 1338.62186

Summary: The goal of this paper is to give recent results in risk theory presented at the Conference “Journée MAS 2012” which took place in Clermont Ferrand. After a brief state of the art on ruin theory, we explore some particular aspects and recent results. One presents matrix exponential approximations of the ruin probability. Then we present asymptotics of the ruin probability based on mixing properties of the claims distribution. Finally, the multivariate case, motivated by reinsurance, is presented and some contemporary results (closed forms and asymptotics) are given.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
62-02 Research exposition (monographs, survey articles) pertaining to statistics

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