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
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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
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