Cont et al. recently showed that coherent risk measures are not robust with respect to changes in large data. In this paper we show that robust risk measures always generate pathological financial positions called "Good Deals". We also introduce the minimal distribution invariant modification of...

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...

In this paper we consider the problem of optimal reinsurance design for general distortion risk measures and premiums. In the first part of the paper, we find the Lagrangian dual of the primal optimal reinsurance problem and show the strong duality holds. Therefore we characterize the optimal...

Motivated by macroeconomic risks, such as the COVID-19 pandemic, we consider different risk management platforms and study efficient insurance schemes in the presence of systematic events. More precisely, we consider three platforms: the risk-sharing, insurance and market platform. First, we...

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...