Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/1920
Title: APPLICATION OF THE SPECTRAL THEORY AND PERTURBATION THEORY TO THE STUDY OF ORNSTEIN-UHLENBECK PROCESSES
Authors: Буртняк, Іван Володимирович
Малицька, Ганна Петрівна
Keywords: spectral theory, singular perturbationtheory, regular perturbationtheory, Sturm-Liouville theory, infinitesimal generator, multidimensional diffusion
Issue Date: 27-Dec-2018
Publisher: Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
Citation: Буртняк I.В., Малицька Г. П. Застосування спектральної теорiї та теорiї збурень до дослiдження процесiв Орнштейна-Уленбека // Карпатськi матем. публ. — 2018. — Т.10, №2. — C. 273–287.
Abstract: The theoretical bases of this paper are the theory of spectral analysis and the theory of singular and regular perturbations. We obtain an approximate price of Ornstein-Uhlenbeck double barrier options with multidimensional stochastic diffusion as expansion in eigenfunctions using infinitesimal generators of a (l + r + 1)-dimensional diffusion in Hilbert spaces. The theorem of accuracy estimation of options prices approximation is established. We also obtain explicit formulas for derivatives price based on the expansion in eigenfunctions and eigenvalues of self-adjoint operators using boundary value problems for singular and regular perturbations
URI: http://hdl.handle.net/123456789/1920
ISSN: 2075-9827
Appears in Collections:Статті та тези (ЕФ)

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