  In this paper, we provide conditions which ensure that stochastic Lipschitz
BSDEs admit Malliavin differentiable solutions. We investigate the problem of
existence of densities for the first components of solutions to general
path-dependent stochastic Lipschitz BSDEs and obtain results for the second
components in particular cases. We apply these results to both the study of a
gene expression model in biology and to the classical pricing problems in
mathematical finance.
