2025/11/05 by Christian Laudagé, Laudagé, Christian, Jörn Saß +1
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #Insurance and Financial Risk Management #Mathematical Finance (q-fin.MF) #Probability and Risk Models #Risk Management (q-fin.RM) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2511.03551
openalex publication_date 2025/11/05 · openalex created_date 2025/11/07 · openalex updated_date 2026/07/28
Under Solvency II, the Value-at-Risk (VaR) is applied, although there is broad consensus that the Expected Shortfall (ES) constitutes a more appropriate risk measure. Moving towards ES would necessitate specifying the corresponding ES level. The recently introduced Probability Equivalent Level of VaR and ES (PELVE) determines this by requiring that ES equals the prescribed VaR for a given future payoff, reflecting the situation of an individual insurer. We incorporate the regulator's perspective by proposing PELVE-inspired methods for multiple insurers. We analyze existence and uniqueness of the resulting ES levels, derive expressions for elliptically distributed payoffs and establish limit results for multivariate regularly distributed payoffs. A case study highlights that the choice of method is crucial when payoffs arise from different distribution families. We provide recommendations which of our PELVE-inspired methods are most appropriate in certain scenarios.