The Bismut-Elworthy-Li formula for semi-linear distribution-dependent SDEs driven by fractional Brownian motion

Abstract: In this work, we will show the existence, uniqueness, and weak differentiability of the solution to semi-linear mean-field stochastic differential equations driven by fractional Brownian motion. We prove an extension of the Bismut-Elworthy-Li formula and show some applications in the sensitivity analysis of variance swaps and also the price of derivatives with respect to the initial point.