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• W2300315546 abstract "This thesis develops some aspects of stochastic calculus via regularization to Banach valued processes. An original concept of Chi-quadratic variation is introduced, where Chi is a subspace of the dual of a tensor product B⊗B where B is the values space of some process X process. Particular interest is devoted to the case when B is the space of real continuous functions defined on [-τ,0], τ>0. Ito formulae and stability of finite Chi-quadratic variation processes are established. Attention is deserved to a finite real quadratic variation (for instance Dirichlet, weak Dirichlet) process X. The C([-τ,0])-valued process X(•) defined by X_t(y) = X_{t+y}, where y ∈ [-τ,0], is called window process. Let T >0. If X is a finite quadratic variation process such that [X]_t = t and h = H(X_T(•)) where H:C([-T,0])→R is L^{2}([-T,0])-smooth or H non smooth but finitely based it is possible to represent h as a sum of a real H_0 plus a forward integral of type int_0^T xi d^-X where H_0 and xi are explicitly given. This representation result will be strictly linked with a function u:[0,T]x C([-T,0])→R which in general solves an infinite dimensional partial differential equation with the property H_{0}=u(0, X_{0}(•)), xi_t=Du(t, X_{t}(•))({0}). This decomposition generalizes important aspects of 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." @default.
• W2300315546 created "2016-06-24" @default.
• W2300315546 creator A5065574081 @default.
• W2300315546 date "2010-07-05" @default.
• W2300315546 modified "2023-09-25" @default.
• W2300315546 title "Calcul stochastique via régularisation en dimension infinie avec perspectives financières" @default.
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