PELVE FROM A REGULATORY PERSPECTIVE

Battle Count: 79

The paper is primarily focused on insurance regulation and Solvency II compliance rather than quantitative trading. However, the VaR-to-ES transition framework, systemic risk measures, and multivariate risk aggregation concepts have indirect relevance for institutional risk management in trading desks. The mathematical tools (elliptical distributions, regularly varying tails) are applicable to portfolio risk assessment but the paper's regulatory framing is specific to insurance.

Implementation requires: (1) Monte Carlo simulation of multivariate equity capital distributions combining Black-Scholes asset models with various liability distributions (gamma, lognormal, GPD); (2) Computation of VaR and ES at multiple levels for each insurer; (3) Numerical optimization for MSE-PELVE (non-convex, potentially non-unique); (4) Handling of multivariate elliptical and regularly varying distributions; (5) Systemic risk aggregation. The theoretical framework is well-defined but practical implementation requires careful numerical handling, especially for the MSE-PELVE optimization and discontinuous PELVE curves from empirical distributions.

The paper provides detailed mathematical definitions, proofs, and parameter specifications for the case study. Monte Carlo simulations (1,000,000 runs) are described. Balance sheet data from six German life insurance companies (2023) are publicly available. However, no code or repository is provided, and the simulation details (random seeds, exact implementation) are not fully specified. The theoretical results are fully reproducible from the mathematical framework.