The obstacle version of the Geometric Dynamic Programming Principle: Application to the pricing of American options under constraints
Bouchard, Bruno; Vu, Thanh Nam (2010), The obstacle version of the Geometric Dynamic Programming Principle: Application to the pricing of American options under constraints, Applied Mathematics and Optimization, 61, 2, p. 235-265. http://dx.doi.org/10.1007/s00245-009-9084-y
TypeArticle accepté pour publication ou publié
Journal nameApplied Mathematics and Optimization
MetadataShow full item record
Vu, Thanh Nam
Abstract (EN)We provide an obstacle version of the Geometric Dynamic ProgrammingPrinciple of Soner and Touzi (J. Eur. Math. Soc. 4:201–236, 2002) for stochastictarget problems. This opens the doors to a wide range of applications, particularly inrisk control in ﬁnance and insurance, in which a controlled stochastic process has tobe 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-hedging cost of American options under portfolio constraints, without appealing tothe standard dual formulation from mathematical ﬁnance. In particular, we allow fora degenerate volatility, a case which does not seem to have been studied so far in thiscontext.
Subjects / KeywordsDiscontinuous viscosity solutions; Stochastic target
Showing items related by title and author.
Bouchard, Bruno (2008) Article accepté pour publication ou publié
Bouchard, Bruno; Chau, Ki; Manai, Arij; Sid-Ali, Ahmed (2019) Article accepté pour publication ou publié
Representation of continuous linear forms on the set of ladlag processes and the pricing of American claims under proportional costs Bouchard, Bruno; Chassagneux, Jean-François (2009) Article accepté pour publication ou publié
On the regularity of the free-boundary in the parabolic obstacle problem. Applications to American options Blanchet, Adrien (2006) Article accepté pour publication ou publié
Generalized stochastic target problems for pricing and partial hedging under loss constraints - Application in optimal book liquidation Bouchard, Bruno; Dang, Ngoc Minh (2013) Article accepté pour publication ou publié