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

June 16, 2026Open Access

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Key Points

The aim is to develop a model for assessing tail risk in incomplete financial markets under restrictive conditions.
Establishes a closed analytical framework for tail risk quantification.
Combines second-order regular variation with functional analysis in Orlicz spaces.
Proves the asymptotic inversion of quantiles using uniform integrability.
Identified that the decay rate of the extreme risk concentration functional follows a power law.
Demonstrated that the uniform integrability of the binomial convolution kernel supports the model's stability.
Validated the ability to compute Conditional Value at Risk using limit-integral exchanges.

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Establishes a model for quantifying tail risk in financial markets, indicating the framework's applicability.

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Roberto Isai Crotone (2026) studied this question.

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