We provide an obstacle version of the Geometric Dynamic Programming Principle of Soner and Touzi (J. Eur. Math. Soc. 4:201–236, 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-hedging cost 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.
Applied Mathematics and Optimization – Springer Journals
Published: Apr 1, 2010
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