Project 5: Restricted Asymptotic Regime Conditional Model. Second-Order Regular Variation and Decay Rate for the Concentration Functional

This paper establishes a closed analytical framework, conditioned on a Restricted Asymptotic Regime, for the segregation and quantification of Tail Risk in incomplete financial markets. Re- nouncing claims of universality over the entire subexponential class, the model is strictly constrained to the dominance of a pure Paretian tail component integrated with the theory of Second-Order Regular Variation (2RV) with a vanishing auxiliary function. The structure merges functional analysis in Orlicz spaces () with F"ollmer-Schweizer orthogonal projections on truncated variables. The framework addresses technical fragilities by explicitly demonstrating the uniform integrability of the binomial convolution kernel and formalizing the asymptotic inversion of the quantile via regular perturbation. These topological guarantees authorize the limit-integral exchange in the computation of the Conditional Value at Risk (CVaR). Assuming the existence of finite higher moments for the hedgeable component and explicit continuity of the quantile function, the exact decay kinematics of the Extreme Risk Concentration Functional are derived. It is formally proven that the distance from unity follows the power law , determining the exponent in the presence of a directional mean shift, and under the hypothesis of a zero mean projection residual in