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After your remarks: So you have 3 lines of business and calculate VaR's for them: $$ VaR_{99.9\%}(L_1) ,VaR_{99.5\%}(L_2) \text{ and } VaR_{99\%}(L_3), $$ so if we speak in terms of events you model at different events - once an event of $0.1\%$ probability and so on. Thus mathematically in my mind it does not make sense to add these VaRs up and see it as ...

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