2 citations · 8 across the 13 of their papers we have counts for
13 papers
Volume estimates and their applications in the problem of optimal recovery
Alexander Kushpel
We study volumes of sections of convex origin-symmetric bodies in induced by orthonormal systems on probability spaces. The approach is based on volume estimates…
Pricing of high-dimensional options
Alexander Kushpel
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatme…
A remark on the trigonometric system
Alexander Kushpel
We present a new property of the trigonometric system arranged in a natural order. It is shown that the sequence of subspaces of trigonometric polynomials is optimal in the sense o…
Polynomials with small norm on compact Riemannian homogeneous manifolds
A. Kushpel
We consider the problem of existence of polynomials with small norm. This range of problems has been extensively studied by many authors in the case of the unit circle (or a compac…
Lebesgue constants on compact manifolds
A. Kushpel
Sharp asymptotic for norms of Fourier projections on two-point homogeneous manifolds (the real sphere, the real, complex and quaternionic projective spaces and the Cayley elliptic…
Entropy of Sobolev's classes on Compact Homogeneous Riemannian Manifolds
A. Kushpel, J. Levesley
We develop a general method to calculate entropy numbers of standard Sobolev's classes on an arbitrary compact homogeneous Riemannian manifold. Our method is essentially based on a…
Approximation of exponential-type functions on a uniform grid by shifts of a basis function
Alexander Kushpel, Jeremy Levesley, Xingping Sun
In this paper, we study the problem of interpolating a continuous function at equally-spaced points in the interval , using shifts of a kernel on the -spaced…
Pricing of basket options II
Alexander Kushpel
We consider the problem of approximation of density functions which is important in the theory of pricing of basket options. Our method is well adopted to the multidimensional case…
Pricing of basket options I
Alexander Kushpel
Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of Lévy driven models of stock markets. In ou…
Density functions in high-dimensional basket options
Alexander Kushpel
We consider an important class of derivative contracts written on multiple assets (so-called spread options) which are traded on a wide range of financial markets. The present pape…
Lévy driven models and derivative pricing
Alexander Kushpel, Jeremy Levesley
We develop a general method for derivative pricing. This approach has its roots in Shannon's Information Theory. The notion of -analyticity of Lévy models is introduced on the b…
Approximation on the complex sphere
Huda Alsaud, Alexander Kushpel, Jeremy Levesley
We develop new elements of harmonic analysis on the complex sphere on the basis of which Bernstein's, Jackson's and Kolmogorov's inequalities are established. We apply these result…
A Multiplier Version of the Bernstein Inequality on the Complex Sphere
Alexander Kushpel, Jeremy Levesley
We prove a multiplier version of the Bernstein inequality on the complex sphere. Included in this is a new result relating a bivariate sum involving Jacobi polynomials and Gegenbau…