Regularity of Generalized Mean-Field G-SDEs
Year: 2025
Type: article
Abstract: We study the regularity properties of the unique solution of a generalized mean-field G-SDE. More precisely, we consider a generalized mean-field G-SDE with a square-integrable random initial condition, establish its first- and second-order Fréchet differentiability in the stochastic initial condition, and specify the G-SDEs of the respective Fréchet derivatives. The first- and second-order Fréchet derivatives are obtained for locally Lipschitz coefficients admitting locally Lipschitz first- and second-order Fréchet derivatives respectively. Our approach heavily relies on the Grönwall inequality, which leverages the Lipschitz continuity of the coefficients.
Source: Mathematics
DOI: 10.3390/math13193099
Authors: Karl-Wilhelm Georg Bollweg, Thilo Meyer-Brandis
Institution: Ludwig-Maximilians-Universität München
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4414610686