A $C^{0,1}$-functional It\^o's formula and its applications in mathematical finance

Bruno Bouchard, Gr\'egoire Loeper and Xiaolu Tan

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Abstract: Using Dupire's notion of vertical derivative, we provide a functional (path-dependent) extension of the It\^o's formula of Gozzi and Russo (2006) that applies to C^{0,1}-functions of continuous weak Dirichlet processes. It is motivated and illustrated by its applications to the hedging or superhedging problems of path-dependent options in mathematical finance, in particular in the case of model uncertainty

Date: 2021-01
New Economics Papers: this item is included in nep-rmg
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