Probabilistic solution of the American options

Details Probabilistic solution of the American options Probabilistic solution of the American options

2008-09-03

arxiv.org/abs/0809.0611v2

Mathematics

Probability

Scientific paper

The existence and uniqueness of probabilistic solutions of variational inequalities for the general American options are proved under the hypothesis of hypoellipticity of the infinitesimal generator of the underlying diffusion process which represents the risky assets of the stock market with which the option is created. The main tool is an extension of the It\^o formula which is valid for the tempered distributions on $\R^d$ and for nondegenerate It\^o processes in the sense of the Malliavin calculus.

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