  We consider an optimal liquidation problem with instantaneous price impact
and stochastic resilience for small instantaneous impact factors. Within our
modelling framework, the optimal portfolio process converges to the solution of
an optimal liquidation problem with general semimartingale controls when the
instantaneous impact factor converges to zero. Our results provide a unified
framework within which to embed the two most commonly used modelling frameworks
in the liquidation literature and provide a microscopic foundation for the use
of semimartingale liquidation strategies and the use of portfolio processes of
unbounded variation. Our convergence results are based on novel convergence
results for BSDEs with singular terminal conditions and novel representation
results of BSDEs in terms of uniformly continuous functions of forward
processes.

Mathematical Finance;Probability