15 citations · 20 across the 6 of their papers we have counts for
6 papers
On statistical estimation and inferences in optional regression models
Mohamed Abdelghani, Alexander Melnikov, Andrey Pak
The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unkno…
Martingale-like sequences in Banach lattices
Haile Gessesse, Alexander Melnikov
Martingale-like sequences in vector lattice and Banach lattice frameworks are defined in the same way as martingales are defined in [Positivity 9 (2005), 437--456]. In these framew…
On mean-variance hedging under partial observations and terminal wealth constraints
Vitalii Makogin, Alexander Melnikov, Yuliya Mishura
In the paper, a mean-square minimization problem under terminal wealth constraint with partial observations is studied. The problem is naturally connected to the mean-variance hedg…
Stochastic viability and comparison theorems for mixed stochastic differential equations
Alexander Melnikov, Yuliya Mishura, Georgiy Shevchenko
For a mixed stochastic differential equation containing both Wiener process and a Hölder continuous process with exponent , we prove a stochastic viability theorem. As a con…
On drift parameter estimation in models with fractional Brownian motion
Yuriy Kozachenko, Alexander Melnikov, Yuliya Mishura
We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum l…
On Financial Markets Based on Telegraph Processes
Nikita Ratanov, Alexander Melnikov
The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occu…