
POSITION
Head of the Department of Probability, Statistics and Actuarial Mathematics
WORK EXPERIENCE
1976–1980
Assistant Professor
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
1980–1986
Lecturer
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
1986–1991
Associate professor
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
1991–2003
Professor
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
2003–Present
Head of the Department of Probability, Statistics and Actuarial Mathematics
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
EDUCATION AND TRAINING
1975
BSc + MSc
Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
1978
PhD
Taras Shevchenko National University of Kiev, Kyiv (Ukraine)
1990
DSc
Taras Shevchenko National University of Kiev, Kyiv (Ukraine)



Stochastic calculus for fractional Brownian motion and related processes, financial mathematics, theory and statistics of random processes and fields, stochastic differential equations
Research Fields:
Mathematics
Previous and Current Research
 Stochastic calculus for fractional Brownian motion
 Financial mathematics· Theory of multiparameter random processes
 Functional limit theorems for random processes and fields
 Martingales and related processes
 Stochastic integration
 Stochastic differential equations
 Optimal stopping problems
 Statistics of the processes with longrange dependence
Yuliia Mishura is the supervisor of the scientific project titled “Investigation and statistical analysis of asymptotic behavior of complex stochastic nonhomogeneous dynamic systems”. The research is concentrated on the development of the theory of processes with longrange dependence, in particular, mixed fractional and multifractional processes, as well as statistical estimation of parameters in fractional and mixed models and option pricing for assets prices of which follow geometrical Brownian motion with longrange dependence.
The team consists of 9 researchers: 1 DSc, 3 PhD candidates and 5 PhD students. We maintain close collaboration with universities of Lausanne, Oslo, Vienna, Montevideo, Sydney, Le Mans, Mannheim and others.
We have made a considerable contribution to stochastic calculus of fractional and multifractional processes, stochastic differential equations and corresponding statistical and financial problems. Particularly, we have investigated classes of multifractional processes, mixed models with longrange dependence and their financial applications. We were the first who obtained general functional limit theorems for multiplicative schemes that are used in financial mathematics.
Now we work on estimation of parameters in mixed models with long and shortrange dependence and multifractional models. We consider approximations for fractional Poisson processes. We estimate parameters of fractional and multifractional process and fields with nonGaussian distributions. We prove functional limit theorems in multiplicative financial schemes with longrange dependence, consider optimal stopping rules, apply Malliavin calculus to financial models.
Future Projects and Goals
 Integral representations of fractional nonGaussian processes
 Parameter estimation in mixed fractional and multifractional models
 Functional limit theorems in multiplicative financial schemes
 Hedging and optimization of markets with longrange dependence
 Properties of random dynamic systems driven by mixed stochastic differential equations
 Properties of statistical estimates for multifractional nonGaussian models
 Approximate methods for mixed stochastic differential equations
 Asymptotic behavior of the solutions of stochastic differential equations
 Optimal stopping problems
Selected Publications
Mishura Y., Ragulina O.
Ruin Probabilities. Smoothness, Bounds, Supermartingale Approach.
Elsevier, ISTE Press, 2016. – 276 p.
Mishura Y.
Financial Mathematics.
Elsevier, ISTE Press, 2016. – 194 p.
Mishura Y.
Maximum likelihood drift estimation for the mixing of two fractional Brownian motions.
Stochastic and Infinite Dimensional Analysis, Eds: Ch. Bernido, M. CarpioBernido, M. Grothaus, T. Kuna, M. J. Oliveira, J. L. da Silva. – 2016. – P. 263280.
Mishura Y., Schied A.
Constructing functions with prescribed pathwise quadratic variation.
Journal of Mathematical Analysis and Applications. – 2016. – Vol. 442 (1). – P. 117137.
Mishura Y., Munchak E.
Rate of convergence of option prices by using the method of pseudomoments.
Theory of Probability and Mathematical Statistics. – 2016. – Vol. 92 (1). – P. 117133.
Melnikov A., Mishura Y., Shevchenko G.
Stochastic viability and comparison theorems for mixed stochastic differential equations.
Methodology and Computing in Applied Probability. – 2015. – Vol. 17 (1). – P. 169188.
Hashorva E., Mishura Y., Seleznev O.
Boundary noncrossing probabilities for fractional Brownian motion with trend.
Stochastics. – 2015. – DOI:10.1080/17442508.2015.1019882.
Mishura Y.
The rate of convergence of option prices on the asset following geometric OrnsteinUhlenbeck process.
Lithuanian Mathematical Journal. – 2015. – Vol. 55 (1). – P. 134149.
Mishura Y.
Diffusion approximation of recurrent schemes for financial markets, with application to the OrnsteinUhlenbeck process.
Opuscula Mathematica. – 2015. – Vol. 35 (1). – P. 99116.
Kozachenko Y., Melnikov A., Mishura Y.
On drift parameter estimation in models with fractional Brownian motion.
Statistics. – 2015. – Vol. 49 (1). – P. 3562.
Mishura Y., Shalajko T., Shevchenko G.
Convergence of solutions of mixed stochastic differential equations with applications.
Applied Mathematics and Computation. – 2015. – Vol. 257. – P. 487497.
Mishura Y., Shevchenko G., Valkeila E.
Random variables as pathwise integrals with respect to fractional Brownian motion.
Stochastic Processes and Their Applications. – 2013. – Vol. 123 (6). – P. 23532369.
Mishura Y., Shevchenko G.
Mixed stochastic differential equations with longrange dependence: existence, uniqueness and convergence of solutions.
Computers and Mathematics with Applications. – 2012. – Vol. 64 (10). – P. 32173227.
Computers and Mathematics with Applications. – 2012. – Vol. 64 (10). – P. 32173227.
The rate of convergence of Hurst index estimate for the stochastic differential equation.
Stochastic Processes and Their Applications. – 2012. – Vol. 122 (11). – P. 37183739.
Mishura Y., Valkeila E.
An extension of the Lévy characterization to fractional Brownian motion.
Annals of Probability. – 2011. – Vol. 39 (2). – P. 439470.
Mishura Y., Melnikov A.
On pricing and hedging in financial markets with longrange dependence.
Mathematics and Financial Economics. – 2011. – Vol. 5 (1). – P. 2946.
Contacts
Homepage: http://probability.univ.kiev.ua/index.php?page=userinfo&person=myus&lan=en
myus@univ.kiev.ua
