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.

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Pages: 612-632

Publication Date: February 27, 2009

DOI: 10.1214/EJP.v14-625

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