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

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.

Domaines: Probabilités [math.PR]

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, 2009, 14, pp.612-632. ⟨hal-00270030⟩