TY - JOUR
AU - Burtnyak, I.V.
AU - Malytska, H.P.
PY - 2018/12/31
Y2 - 2023/09/25
TI - Application of the spectral theory and perturbation theory to the study of Ornstein-Uhlenbeck processes
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 10
IS - 2
SE - Scientific articles
DO - 10.15330/cmp.10.2.273-287
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/1487
SP - 273-287
AB - 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.
ER -