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

Abstract

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

Keywords

• glue value-at-risk
• distributional robustness reinsurance
• uncertainty
• four-point distribution
• stop-loss