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.