11 citations · 27 across the 7 of their papers we have counts for
7 papers
Lie symmetries of fundamental solutions of one (2+1)-dimensional ultra-parabolic Fokker--Planck--Kolmogorov equation
Sergii Kovalenko, Valeriy Stogniy, Maksym Tertychnyi
A (2+1)-dimensional linear ultra-parabolic Fokker--Planck--Kolmogorov equation is investigated from the group-theoretical point of view. By using the Berest--Aksenov approach, an a…
Currency Derivatives Pricing for Markov-modulated Merton Jump-diffusion Spot Forex Rate
Anatoliy Swishchuk, Maksym Tertychnyi, Winsor Hoang
We derived similar to Bo et al. (2010) results but in the case when the dynamics of the FX rate is driven by a general Merton jump-diffusion process. The main results of our paper…
Pricing Currency Derivatives with Markov-modulated Levy Dynamics
Anatoliy Swishchuk, Maksym Tertychnyi, Robert Elliott
Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for…
On quasi-continuous approximation in classical statistical mechanics
Sergey Petrenko, Alexei Rebenko, Maksym Tertychnyi
A continuous infinite system of point particles with strong superstable interaction is considered in the framework of classical statistical mechanics. The family of approximated co…
Quasi-lattice approximation of statistical systems with strong superstable interactions. Correlation functions
Alexei Rebenko, Maksym Tertychnyi
A continuous infinite system of point particles interacting via two-body strong superstable potential is considered in the framework of classical statistical mechanics. We define s…
On stability, superstability and strong superstability of classical systems of Statistical Mechanics
Oleksey Rebenko, Maksym Tertychnyi
A detailed analysis of conditions on 2-body interaction potential, which ensure stability, superstability or strong superstability of statistical systems is given. There has been g…