Open AccessApplication of the spectral theory and perturbation theory to the study of Ornstein-Uhlenbeck processes
Author(s) -
Ivan Burtnyak,
H.P. Malytska
Publication year - 2018
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.10.2.273-287
Subject(s) - mathematics , eigenfunction , singular perturbation , eigenvalues and eigenvectors , spectral theory , hilbert space , mathematical analysis , boundary value problem , infinitesimal , ornstein–uhlenbeck process , perturbation theory (quantum mechanics) , stochastic process , physics , statistics , quantum mechanics
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.