Euler Allocations in the Presence of Non-Linear Reinsurance : Comment on Major (2018)

Major (2018) discusses Euler/Aumann-Shapley allocations for non-linear portfolios. He argues convincingly that many (re)insurance portfolios, while non-linear, are nevertheless positively homogeneous, owing to the way that deductibles and limits are typically set. For such non-linear but homogeneous portfolio structures, he proceeds with defining and studying a particular type of capital allocation. In this comment, we build on Major's (2018) insights but take a slightly different direction, to consider Euler capital allocations for distortion risk measures applied to homogeneous portfolios. Thus, the important problem of capital allocation in portfolios with non-linear reinsurance is solved