The randomly distorted Choquet integrals with respect to a G-randomly distorted capacity and risk measures

Battle Count: 61

The paper provides a rigorous theoretical foundation for risk measures under model ambiguity (capacity framework), which is relevant for quantitative risk management in trading. The randomised VaR and AVaR extensions could inform conditional risk assessment in regime-switching markets. However, the paper is purely theoretical with no direct trading strategy, backtesting, or empirical application. The connection to practical quantitative trading is indirect, primarily through the risk measurement framework that could inform position sizing and capital allocation under ambiguity.

Extremely high complexity. The paper requires deep knowledge of non-additive measure theory, Choquet integration, capacity theory, stochastic orderings, and functional analysis. Implementation would require: (1) constructing capacities on measurable spaces, (2) defining and verifying G-random distortion functions, (3) computing Choquet integrals with respect to distorted capacities, (4) verifying comonotonicity conditions, (5) working with quantile functions relative to capacities. The theoretical nature means there is no straightforward code implementation without significant mathematical infrastructure.

This is a purely theoretical mathematics paper with complete proofs provided for all theorems, propositions, and lemmas. All definitions are self-contained, and the mathematical framework is fully specified. The proofs in the Appendix cover technical lemmas. No computational experiments or data are involved, making the results fully verifiable through mathematical reasoning.