Risk management in complex financial institutions is usually implemented as a two-stage process. First, a total capital requirement (the aggregate risk margin) is computed at the corporate level; then, consistent with business targets and/or solvency considerations, this total is apportioned across several more granular units (risk capital allocation). For an insurance company, these units may represent agents, business lines, or specific guarantees embedded in a set of contracts; the total capital should be a positive margin, and the resulting shares should all be positive and sum to one (full allocation). In this framework, the capital shares can be viewed as parts of a whole, subject to a unit-sum constraint: this interpretation suggests a natural connection between capital allocation rules and principles of Compositional Data (CoDa) analysis. Prioritizing the compositional perspective, this work introduces a new optimality criterion for proportional risk capital allocations in insurance contexts. The proposed rule requires that capital shares assigned to individual units should be "sufficiently close" to the corresponding loss proportions in a metric that is compatible with the Aitchison distance on the simplex. We solve this optimization problem for corporate- or market-driven risk scenarios aligned with realistic managerial concerns, and we investigate the behavior of the resulting CoDa allocations under different distributional assumptions and dependence structures among risks. The outcomes of some numerical studies, including an empirical application to a public database of cyber losses, suggest that CoDa methods can offer a valuable alternative to traditional allocation rules, particularly when heavy-tailed risks are present or market conditions call for flexible allocation schemes based on proportional rather than absolute risk contributions from distinct sources.
Zoom link: https://uoc-gr.zoom.us/j/88177475079?pwd=ik9vJRdyknP8xneS5NumlqgQdnplaz.1
