Improving Marginal Expected Shortfall estimates using credibility methods

Marginal Expected Shortfall (MES) is widely regarded as a key indicator for systemic risk measurement, as it reflects the vulnerability of individual institutions under market stress. Yet conventional MES estimators may become unstable and highly variable when tail observations are limited or confidence levels are high. To mitigate this issue, a credibility-based estimator is introduced, where empirical tail information is combined with prior knowledge through an optimally determined weighting scheme. The resulting closed-form expression improves numerical stability and reduces variance while avoiding posterior simulation. Monte Carlo experiments with lower-tail-dependent copulas confirm its convergence and show lower sampling variability, particularly in small-sample and high-confidence settings. An empirical application to the CSI 300 index and five A-share stocks further demonstrates its ability to capture cross-sectoral heterogeneity in systemic risk, with a data-driven calibration of prior information enhancing practical relevance for regulators and risk managers.