Distributionally Robust Reinsurance with Glue Value-at-Risk and Expected Value Premium

In this paper, we explore a distributionally robust reinsurance problem that incorporates the concepts of Glue Value-at-Risk and expected value premium principle. The focuses on stop-loss contracts with known mean variance loss. optimization can be formulated as minimax problem, where inner involves maximizing over all distributions same variance. It is demonstrated represented either three-point under some mild condition or four-point otherwise. Additionally, analytical solutions are provided for determining optimal deductible values.