52 citations · 535 across the 39 of their papers we have counts for
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Pricing double barrier options on homogeneous diffusions: a Neumann series of Bessel functions representation
Igor V. Kravchenko, Vladislav V. Kravchenko, Sergii M. Torba +1
This paper develops a novel analytically tractable Neumann series of Bessel functions representation for pricing (and hedging) European-style double barrier knock-out options, whic…
On construction of transmutation operators for perturbed Bessel equations
Vladislav V. Kravchenko, Elina L. Shishkina, Sergii M. Torba
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with co…
Transmutation operators: construction and applications
Vladislav V. Kravchenko, Sergii M. Torba, Kira V. Khmelnytskaya
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Sc…
Analytic approximation of solutions of parabolic partial differential equations with variable coefficients
Vladislav V. Kravchenko, Josafath A. Otero, Sergii M. Torba
A complete family of solutions for the one-dimensional reaction-diffusion equation \[ u_{xx}(x,t)-q(x)u(x,t) = u_t(x,t) \] with a coefficient depending on is constructed. T…
Solution of parabolic free boundary problems using transmuted heat polynomials
Igor V. Kravchenko, Vladislav V. Kravchenko, Sergii M. Torba
A numerical method for free boundary problems for the equation \[ u_{xx}-q(x)u=u_t \] is proposed. The method is based on recent results from transmutation operators theory allowin…
Asymptotics with respect to the spectral parameter and Neumann series of Bessel functions for solutions of the one-dimensional Schrödinger equation
Vladislav V. Kravchenko, Sergii M. Torba
A representation for a solution of the equation , satisfying the initial conditions , is derived in the form \[ u(ω,x)=e^{iωx}\left…