Representation of continuous linear forms on the set of ladlag processes and the hedging of American claims under proportional costs
Jean-Francois Chassagneux, ENSAE
Bruno Bouchard, Université Paris Dauphine, Ceremade
Abstract
We discuss a d-dimensional version (for lądląg optional
processes) of a duality result by Meyer (1976) between
{bounded} cądląg adapted processes and random measures. We show
that it allows to establish, in a very natural way, a dual
representation for the set of initial endowments which allow to
super-hedge a given American claim in a continuous time model
with proportional transaction costs. It generalizes a previous
result of Bouchard and Temam (2005) who considered a discrete
time setting. It also completes the very recent work of Denis, De
Valličre and Kabanov (2008) who studied cądląg American claims and
used a completely different approach.
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