New results for additive and multiplicative risk apportionment (Q2201712)

The paper presents new characterizations of the preference for additive and multiplicative risk apportionment when risk orderings involves stochastic dominance. After providing the basic definitions and concepts about additive and multiplicative risks, together with the main characterization theorems, the authors develop some results on additive risks, particularly concerning equivalence between risk apportionment at orders $s_1$ and $s_2$ and risk apportionment at orders $s'_1$ and $s'_2$ when $s_1+s_2=s'_1+s'_2$. Moreover, they focus on risk apportionment in a multiplicative risks context and set their previous results within this context. Successively, the authors specifically deepen the preference for multiplicative risk apportionment at orders $s_1$ and $s_2\geq s_1$, that is sufficient for the preference to hold at orders $s'_1=s_1-1$ and $s'_2=s_2+1$, as well as the case where $s_1=2$. Finally the case of CRRA utility functions is considered. An Appendix contains the technical details of the results presented in the paper.