On the Expected Maximum Deficit and the Optimal Allocation of Reserves

Battle Count: 78

The paper is primarily focused on actuarial insurance risk management and reserve allocation. While the distortion risk measure framework and path-dependent risk concepts have some theoretical overlap with quantitative finance (e.g., VaR/AVaR of running maxima), the paper does not address trading strategies, market microstructure, or asset pricing. The liquidity interpretation of EMD could tangentially relate to funding risk in trading desks, but this is not the paper's focus.

Implementation requires: (1) understanding of Choquet integrals and distortion risk measures, (2) Monte Carlo simulation of joint loss paths with Poisson-gamma counts and empirical resampling, (3) numerical inversion of deficit functions for tolerance-based measures, (4) convex optimization on the simplex for allocation (water-filling for Method 1, subgradient methods for Method 2), (5) handling of Lambert W functions for closed-form benchmarks, and (6) careful treatment of conditional risk measures and review-date reallocation. The theoretical framework is sophisticated but the computational methods are well-defined.

The paper provides an accompanying R script (danishmulti_emdallocation.R) that reproduces paths, allocation table, simplex figure, and diagnostics. The Danish fire-loss dataset (danishmulti) is publicly available via the CASdatasets R package. Closed-form solutions are provided for exponential benchmarks. Monte Carlo estimators are fully specified. However, some implementation details (e.g., exact random seeds, full code listing) are not in the paper text itself.