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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 24 open journal systems 


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 làdlàg optional processes) of a duality result by Meyer (1976) between {bounded} càdlàg 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 Vallière and Kabanov (2008) who studied càdlàg American claims and used a completely different approach.


Full text: PDF

Pages: 612-632

Published on: February 27, 2009
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Electronic Journal of Probability. ISSN: 1083-6489