Application of the spectral theory and perturbation theory to the study of Ornstein-Uhlenbeck processes

  • I.V. Burtnyak Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • H.P. Malytska Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0002-5811-9288
Keywords: spectral theory, singular perturbation theory, regular perturbation theory, Sturm-Liouville theory, infinitesimal generator, multidimensional diffusion
Published online: 2018-12-31

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.

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How to Cite
(1)
Burtnyak I., Malytska H. Application of the Spectral Theory and Perturbation Theory to the Study of Ornstein-Uhlenbeck Processes. Carpathian Math. Publ. 2018, 10 (2), 273-287.