Representation of continuous linear forms on the set of ladlag processes and the pricing of American claims under proportional costs

Bruno Bouchard 1, 2 Jean-François Chassagneux 1, 3
1 LFA - Laboratoire de Finance Assurance
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
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 restricted to càdlàg American claims and used a completely different approach.
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Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2009, 14, pp.612-632
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Bruno Bouchard, Jean-François Chassagneux. Representation of continuous linear forms on the set of ladlag processes and the pricing of American claims under proportional costs. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2009, 14, pp.612-632. 〈hal-00270030〉

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