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Following some recent works on risk aggregation and capital allocation formixed Erlang risks joined by Sarmanov's multivariate distribution, in thispaper we present some closed-form formulas for the same topic by considering,however, a different kernel function for Sarmanov's distribution, notpreviously studied in this context. The risk aggregation and capital allocationformulas are derived and numerically illustrated in the general framework ofstop-loss reinsurance, and then in the particular case with no stop-lossreinsurance. A discussion of the dependency structure of the considereddistribution, based on Pearson's correlation coefficient, is also presented fordifferent kernel functions and illustrated in the bivariate case.

On some multivariate Sarmanov mixed Erlang reinsurance risks: aggregation and capital allocation