Spectral Analysis of Countable Families of Commuting Self-Adjoint Operators (CSO)

1991 ◽  
pp. 7-40
Author(s):  
Y. S. Samoilenko
Keyword(s):  
Spectral Analysis ◽  
Adjoint Operators

THE SPECTRAL ANALYSIS OF SELF-ADJOINT OPERATORS

1945 ◽  
Vol os-16 (1) ◽  
pp. 31-48
Author(s):  
J. L. B. COOPER
Keyword(s):  
Spectral Analysis ◽  
Adjoint Operators

Spectral analysis of some non-self-adjoint operators

1981 ◽  
Vol 33 (2) ◽  
pp. 177-181 ◽  
Author(s):  
E. V. Cheremnykh
Keyword(s):  
Spectral Analysis ◽  
Adjoint Operators

Spectral Analysis of Self-adjoint Operators

2012 ◽  
pp. 177-206
Author(s):  
D. M. Gitman ◽  
I. V. Tyutin ◽  
B. L. Voronov
Keyword(s):  
Spectral Analysis ◽  
Adjoint Operators

scholarly journals Modelling of derivatives pricing using methods of spectral analysis

2020 ◽  
Vol 7 (3) ◽  
pp. 128-136
Author(s):  
Ivan Burtnyak ◽  
Anna Malytska
Keyword(s):  
Spectral Analysis ◽  
Stock Market ◽  
Spectral Theory ◽  
Asset Price ◽  
Analytical Formula ◽  
Wave Theory ◽  
Financial Instruments ◽  
Derivatives Pricing ◽  
Financial Flows ◽  
Adjoint Operators

In this article expands the method of finding the approximate price for a wide class of derivative financial instruments. Using the spectral theory of self-adjoint operators in Hilbert space and the wave theory of singular and regular perturbations, the analytical formula of the approximate asset price is established. Methods for calculating the approximate price of options using the tools of spectral analysis, singular and regular wave theory in the case of fast and slow factors are developed. Combining methods from the spectral theory of singular and regular perturbations, it is possible to estimate the price of derivative financial instruments as a schedule by eigenfunctions. The approximate value of securities and their rate of return are calculated. Applying the theory of Sturm-Liouville, Fredholm’s alternative and analysis of singular and regular perturbations at different time scales have enabled us to obtain explicit formulas for the approximate value of securities and their yield on the basis of the development of their eigenfunctions and eigenvalues of self-adjoint operators using boundary value problems for singular and regular perturbations. The theorem of closeness estimates for bond prices approximation is proved. An algorithm for calculating the approximate price of derivatives and the accuracy of estimates has been developed, which allows to analyze and draw precautionary conclusions and suggestions to minimize the risks of pricing derivatives that arise in the stock market. A model for finding the value of derivatives corresponding to the dynamics of the stock market and the size of financial flows has been developed. This model allows you to find the prices of derivatives and their volatility, as well as minimize speculative changes in pricing, analyze the progress of stock market processes and take concrete steps to improve the situation to optimize financial strategies. The used methodology of European options pricing based on the study of volatility behavior and analysis of the yield of financial instruments allows to increase the accuracy of the forecast and make sound management strategic decisions by stock market participants.

INTERACTING FOCK SPACES AND THE MOMENTS OF THE LIMIT DISTRIBUTIONS FOR QUANTUM RANDOM WALKS

2013 ◽  
Vol 16 (01) ◽  
pp. 1350003 ◽  
Author(s):  
CHUL KI KO ◽  
HYUN JAE YOO
Keyword(s):  
Spectral Analysis ◽  
Random Walks ◽  
Vacuum Expectation ◽  
High Dimensional ◽  
Fock Spaces ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
Limit Distributions ◽  
Time Quantum ◽  
Adjoint Operators

We investigate the limit distributions of the discrete time quantum random walks on lattice spaces via a spectral analysis of concretely given self-adjoint operators. We discuss the interacting Fock spaces associated with the limit distributions. Thereby, we represent the moments of the limit distribution by vacuum expectation of the monomials of the Fock operator. We get formulas not only for one-dimensional walks but also for high-dimensional walks.

Spectral analysis of asymmetry training effect for depression

2008 ◽  
Author(s):  
Ji Ha Lee ◽  
Sung Won Choi ◽  
Ji Sun Min ◽  
Eun Ju Jaekal ◽  
Gyhye Sung
Keyword(s):  
Spectral Analysis ◽  
Training Effect
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