On Some Multivariate Sarmanov Mixed Erlang Reinsurance Risks: Aggregation and Capital Allocation
20 Pages Posted: 14 Nov 2016
Date Written: November 13, 2016
Following some recent works on risk aggregation and capital allocation for mixed Erlang risks joined by Sarmanov's multivariate distribution, in this paper we present some closed-form formulas for the same topic by considering, however, a different kernel function for Sarmanov's distribution, not previously studied in this context. The risk aggregation and capital allocation formulas are derived and numerically illustrated in the general framework of stop-loss reinsurance, and then in the particular case with no stop-loss reinsurance. A discussion of the dependency structure of the considered distribution, based on Pearson's correlation coefficient, is also presented for different kernel functions and illustrated in the bivariate case.
Keywords: Sarmanov distribution, Mixed Erlang distribution, Capital allocation, Risk aggregation, Stop-loss reinsurance, Dependency
JEL Classification: C46, G22
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