Tobias von Petersdorff

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A partial integro-differential equation (PIDE) ∂ t u + A[u] = 0 for European contracts on assets with general jump-diffusion price process of Lévy type is derived. The PIDE is localized to bounded domains and the error due to this localization is estimated. The localized PIDE is discretized by the θ-scheme in time and a wavelet Galerkin method with N(More)
We consider elliptic and parabolic variational equations and inequalities governed by integro-differential operators of order 2s ∈ (0, 2]. Our main motivation is the pricing of European or American options under Lévy processes, in particular pure jump processes or jump diffusion processes with tempered stable processes. The problem is discretized using(More)
Galerkin discretizations of integral operators in ℝ d $\mathbb {R}^{d}$ require an accurate numerical evaluation of integrals I = ∫ S ( 1 ) ∫ S ( 2 ) f ( x , y ) dydx $I={\int }_{\!\!S^{(1)}}{\int }_{\!\!S^{(2)}}f(x,y)dydx$ where S (1), S (2) are d-simplices and the integrand function f has a possibly nonintegrable singularity at x = y. In a previous paper(More)
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