The Obstacle version of the Geometric Dynamic Programming Principle : Application to the pricing of American options under constraints

Bruno Bouchard (1, 2) , Than Nam Vu (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CREST - Centre de Recherche en Économie et Statistique

We provide an American version of the Geometric Dynamic Programming Principle of Soner and Touzi (2002) for stochastic target problems. This opens the doors to a wide range of applications, particularly in risk control in finance and insurance, in which a controlled stochastic process has to be maintained in a given set on a time interval [0,T]. As an example of application, we show how it can be used to provide a viscosity characterization of the super-heging price of American options under portfolio constraints, without appealing to the standard dual formulation from mathematical finance. In particular, we allow for a degenerate volatility, a case which does not seem to have been studied so far in this context.

Mots clés: Stochastic target; American options

Domaines: Probabilités [math.PR]

Bruno Bouchard, Than Nam Vu. The Obstacle version of the Geometric Dynamic Programming Principle : Application to the pricing of American options under constraints. Applied Mathematics and Optimization, 2010, 61 (2), pp.235-265. ⟨10.1007/s00245-009-9084-y⟩. ⟨hal-00343816⟩