  For portfolio optimisation under proportional transaction costs, we provide a
duality theory for general cadlag price processes. In this setting, we prove
the existence of a dual optimiser as well as a shadow price process in a
generalised sense. This shadow price is defined via a "sandwiched" process
consisting of a predictable and an optional strong supermartingale and pertains
to all strategies which remain solvent under transaction costs. We provide
examples showing that in the present general setting the shadow price process
has to be of this generalised form.
