Abstract
We derive stochastic Leibniz formulas for Volterra integrals under enlarged filtrations. We investigate both pure-jump and Brownian Volterra processes under diverse initially enlarged filtration approaches. In these settings, we compare the ordinary with the stochastic (Doleans-Dade) exponential of a Volterra process and provide the corresponding martingale conditions. We also consider backward stochastic Volterra integral equations (BSVIEs) under enlarged filtrations and obtain the related solution formulas. We finally propose an anticipative Heath Jarrow Morton (HJM) forward rate model of Volterra-type. In an introductory section, we compile various facts on deterministic and stochastic Leibniz formulas for parameter integrals.
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