and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a … the risk of extreme events since they appear as a natural extension of multivariate extreme-value theory to the level of …An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities …

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 reinsurance policies by solving the dual problem and we will see that the …

In this paper, we study two classes of optimal reinsurance models by minimizing the total risk exposure of an insurer … under the criteria of value at risk (VaR) and conditional value at risk (CVaR). We assume that the reinsurance premium is …-continuous retained loss functions, the truncated stop-loss reinsurance is shown to be optimal. In contrast, under CVaR risk measure, the …

This paper unifies the work on multiple reinsurers, distortion risk measures, premium budgets,and heterogeneous beliefs …. An insurer minimizes a distortion risk measure, while seekingreinsurance with finitely many reinsurers. The reinsurers … distribution.We provide a characterization of optimal reinsurance indemnities, and we show that they are ofa layer-insurance type …