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

2022/09/12 by Tahmasebi, M.
#60G22 (secondary) #60H10 (primary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2209.05586

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.

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