Capital-Allocation-Induced Risk Sharing

Battle Count: 64

The paper is primarily relevant to risk management rather than direct trading strategies. However, it has indirect relevance: (1) capital allocation across trading desks is a core banking function; (2) VaR and distortion risk measures are fundamental in quantitative risk management; (3) the framework could inform how trading desks share portfolio risk; (4) the connection between Euler capital allocation and risk sharing could be applied to multi-strategy fund risk budgeting. The paper does not address trading signals, execution, or alpha generation directly.

High complexity due to: (1) requirement for measurable right-invertibility of aggregate capital functions; (2) need to solve parametric families of optimization problems; (3) closed-form solutions only available for specific cases (elliptical distributions, specific distortion functions); (4) numerical implementation requires careful handling of quantile functions, distortion functions, and their inverses; (5) the framework involves multiple layers of abstraction (parametrization, inversion, randomization); (6) no reference implementation or code is provided.

The paper is purely theoretical with complete mathematical proofs provided in appendices. All formulas are explicitly derived. However, no code, software implementation, or empirical datasets are provided. Numerical examples use simulated data from specified distributions (Gamma, elliptical, copula-based) but no code is shared. Reproduction requires implementing the mathematical framework from scratch.