What is it about?
We prove rigorously that the intuitive probabilistic solution of the free boundary problem for American options is in fact the true mathematical solution if the underlying diffusion process ism non-degenerate in the sense of the Malliavin Calculus. To achieve this we use also an Ito formula which expresses a tempered distribution combined with a non-degenerate diffusion.
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Why is it important?
This is the sole rigorous solution of this problem.
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This page is a summary of: Probabilistic solution of the American options, Journal of Functional Analysis, May 2009, Elsevier,
DOI: 10.1016/j.jfa.2008.10.016.
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