Boundary Layers and Heavy Tails in Finance

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Résumé

This paper proposes a unified framework combining Extreme Value Theory (EVT) and nonlinear partial differential equations to model financial returns on the BRVM. We conjecture a link between the EVT tail index ξ and the p-Laplacian exponent p: ξ=1/(p−1) . The conjecture is motivated by a heuristic boundary layer analysis (which suggests ξ=1/p ) but empirical fit on 20 BRVM assets unambiguously yields ξ=1/(p−1) . Using independent numerical estimation of p (via the SBA method) and ξ (via GPD), we find excellent agreement. Results show strong heterogeneity across sectors, with agriculture exhibiting the heaviest tails (ξ up to 0.56) and violation of mean reversion. A stress-testing grid is proposed for regulators.

Mots-clés

p-Laplacian, Extreme Value Theory, Boundary Layer, BRVM, Financial Returns, Value-at-Risk