Optimal Reinsurance under the Linear Combination of Risk Measures in the Presence of Reinsurance Loss Limit

Optimal reinsurance problems under the risk measures, such as Value-at-Risk (VaR) and Tail-Value-at-Risk (TVaR), have been studied in recent literature. However, losses based on VaR may be underestimated TVaR allows us to account better for catastrophic losses. In this paper, we propose a new family of flexible measures denoted by LVaR, which is weighted combination TVaR. Based deal with optimal problem minimizing LVaR total risks an insurer when two types constraints reinsurer’s exposure are considered. The results indicate that two-layer always policy both constraints. Also, find depends confidence level, weight coefficient, safety loading, tolerance well relations between them. Finally, illustrate numerical examples compare them Lu et al.