This paper gives a general formulation of systematic risk in a risk pool and studies its relation with principle of insurance (POI), its extension principle of pooling (POP), and valuation. We will see that the systematic risk is secure if and only if POP holds. We call this proposition the...

The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for Choquet risk measures, we give some necessary and sufficient conditions for the existence of optimal and asymptotic optimal...

Motivated by reinsurance applications, we consider an optimal risk sharing problem for individual risks. In a framework where the market participants' preferences are according to the sub-additive and law-invariant risk measures, first we characterize the optimal individual risk sharing...