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Youssouf, M., Moussa, B., Pare, Y. and Some, B. (2019) Solving a Few Linear Partial Differential Equations (PDEs) of Cauchy Kind by the SBA Method. Advances in Differential Equations and Control Processes, 20, 115-128.
https://doi.org/10.17654/de020010115

has been cited by the following article:

• TITLE: Boundary Layers and Heavy Tails in Finance

  AUTHORS: Mamadou Birba, Moussa Bagayogo, Vini Yves Bernadin Loyara

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

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.16 No.9, September 17, 2026

  ABSTRACT: 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.