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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

Type
Article accepté pour publication ou publié
Date
2010
Journal name
Applied Mathematics and Optimization
Volume
61
Number
2
Publisher
Springer
Pages
235-265
Publication identifier
http://dx.doi.org/10.1007/s00245-009-9084-y
Metadata
Show full item record
Author(s)
Bouchard, Bruno
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 / Keywords
Discontinuous viscosity solutions; Stochastic target

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