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On the cumulative parisian ruin of multi-dimensional Brownian motion risk models. (English) Zbl 1454.91196

Summary: Consider a multi-dimensional Brownian motion which models the surplus processes of multiple lines of business of an insurance company. Our main result gives exact asymptotics for the cumulative Parisian ruin probability as the initial capital tends to infinity. An asymptotic distribution for the conditional cumulative Parisian ruin time is also derived. The obtained results on the cumulative Parisian ruin can be seen as generalisations of some of the results derived in K. Dȩbicki et al. [Stochastic Processes Appl. 128, No. 12, 4171–4206 (2018; Zbl 1417.60028)]. As a particular interesting case, the two-dimensional Brownian motion risk model is discussed in detail.

MSC:

91G05 Actuarial mathematics
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)

Citations:

Zbl 1417.60028
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References:

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