Risk measures and multivariate extensions of Breiman’s theorem. (English) Zbl 1246.91060
The authors consider discrete-time insurance risk models with finite time horizon and obtain asymptotics of the ruin probability by means of sum of the tail probabilities of individual claim amounts under different dependence settings for the claim amounts and discount factors. More precisely, they investigate asymptotics of ruin probability under multivariate regular variation and derive them from extensions of Breiman’s theorem. They thus present new situations where the ruin probability admits computable equivalents. Similar asymptotics are also derived for the value at risk.
Reviewer: Pavel Stoynov (Sofia)
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
Keywords:
discrete-time model; ruin probability; value at risk; multivariate regular variation; dependent riskReferences:
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