Seminario: 4 Maggio 2016 - Cristina Di Girolami
Mercoledì 4 Maggio 2016, ore 13:00 presso l'Aula di Matematica (Sapienza Università di Roma, Dipartimento MEMOTEF, Via del Castro Laurenziano 9, Roma - Facoltà di Economia, 1° piano)
la dott.ssa Cristina Di Girolami (Università di Chieti-Pescara)
terrà un seminario dal titolo: Infinite dimensional calculus via regularization with financial motivations, an infinite dimensional PDE and some stability results.
This talk develops some recent results on result for path dependent PDE. In order to solve this problem some aspects of stochastic calculus via regularization to Banach valued processes will be recalled. An original concept of chi-quadratic variation is introduced, where chi is a subspace of the dual of a tensor product B with itself, where B is the values space of the process. Particular interest is devoted to the case when B is the space of real continuous functions defined on [-T; 0], T> 0. Itô formulae and stability of finite -quadratic variation processes are established. Attention is devoted to a finite real quadratic variation (for instance Dirichlet, weak Dirichlet) process X. The C([-T; 0])-valued process X(•) defined by values of process X with its past. Let T > 0. A representation result will be strictly linked to a real valued function u : [0; T] X C([-T; 0]) solving an infinite dimensional path dependent partial differential equation with some explicit formula for a decomposition result of type Clark-Ocone formula which is true when X is the standard Brownian motion W. The financial perspective of this work is related to hedging theory of path dependent options without semimartingales.