30 research outputs found
Spectral expansions of cosmological fields
We give a review of the theory of random fields defined on the observable
part of the Universe that satisfy the cosmological principle, i.e., invariant
with respect to the 6-dimensional group of the isometries of the
time slice of the Friedmann--Lema\^{\i}tre--Robertson--Walker standard chart.
Our new results include proof of spectral expansions of scalar and spin
weighted -invariant cosmological fields in open, flat, and closed
cosmological models.Comment: 24 pages, no figure
Adapted Downhill Simplex Method for Pricing Convertible Bonds
The paper is devoted to modeling optimal exercise strategies of the behavior
of investors and issuers working with convertible bonds. This implies solution
of the problems of stock price modeling, payoff computation and min-max
optimization.
Stock prices (underlying asset) were modeled under the assumption of the
geometric Brownian motion of their values. The Monte Carlo method was used for
calculating the real payoff which is the objective function. The min-max
optimization problem was solved using the derivative-free Downhill Simplex
method.
The performed numerical experiments allowed to formulate recommendations for
the choice of appropriate size of the initial simplex in the Downhill Simplex
Method, the number of generated trajectories of underlying asset, the size of
the problem and initial trajectories of the behavior of investors and issuers.Comment: 18 pages, 8 figure
Matérn class tesor-valued random fields and beyond
We construct classes of homogeneous random fields on a three-dimensional Euclidean
space that take values in linear spaces of tensors of a fixed rank and are
isotropic with respect to a fixed orthogonal representation of the group of 3 × 3 orthogonal
matrices. The constructed classes depend on finitely many isotropic spectral
densities. We say that such a field belong to either the Matérn or the dual Matérn
class if all of the above densities are Matérn or dual Matérn. Several examples are
considered
An optimal series expansion of the multiparameter fractional Brownian motion
We derive a series expansion for the multiparameter fractional Brownian
motion. The derived expansion is proven to be rate optimal.Comment: 21 pages, no figures, final version, to appear in Journal of
Theoretical Probabilit