Yuliia Mishura




Yuliia Mishura

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 long-range dependence

Yuliia Mishura is the supervisor of the scientific project titled “Investigation and statistical analysis of asymptotic behavior of complex stochastic non-homogeneous dynamic systems”. The research is concentrated on the development of the theory of processes with long-range 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 long-range 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 long-range 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 short-range dependence and multifractional models. We consider approximations for fractional Poisson processes. We estimate parameters of fractional and multifractional process and fields with non-Gaussian distributions. We prove functional limit theorems in multiplicative financial schemes with long-range dependence, consider optimal stopping rules, apply Malliavin calculus to financial models.

Future Projects and Goals

  •  Integral representations of fractional non-Gaussian processes
  •  Parameter estimation in mixed fractional and multifractional models
  •  Functional limit theorems in multiplicative financial schemes
  •  Hedging and optimization of markets with long-range dependence
  •  Properties of random dynamic systems driven by mixed stochastic differential equations
  •  Properties of statistical estimates for multifractional non-Gaussian 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. Carpio-Bernido, M. Grothaus, T. Kuna, M. J. Oliveira, J. L. da Silva. – 2016. – P. 263-280.

Mishura Y., Schied A.
Constructing functions with prescribed pathwise quadratic variation.
Journal of Mathematical Analysis and Applications. – 2016. – Vol. 442 (1). – P. 117-137.

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. 117-133.

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. 169-188.

Hashorva E., Mishura Y., Seleznev O.
Boundary non-crossing 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 Ornstein-Uhlenbeck process.
Lithuanian Mathematical Journal. – 2015. – Vol. 55 (1). – P. 134-149.

Mishura Y.
Diffusion approximation of recurrent schemes for financial markets, with application to the Ornstein-Uhlenbeck process.
Opuscula Mathematica. – 2015. – Vol. 35 (1). – P. 99-116.

Kozachenko Y., Melnikov A., Mishura Y.
On drift parameter estimation in models with fractional Brownian motion.
Statistics. – 2015. – Vol. 49 (1). – P. 35-62.

Mishura Y., Shalajko T., Shevchenko G.
Convergence of solutions of mixed stochastic differential equations with applications.
Applied Mathematics and Computation. – 2015. – Vol. 257. – P. 487-497.

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. 2353-2369.

Mishura Y., Shevchenko G.
Mixed stochastic differential equations with long-range dependence: existence, uniqueness and convergence of solutions.
Computers and Mathematics with Applications. – 2012. – Vol. 64 (10). – P. 3217-3227.

Computers and Mathematics with Applications. – 2012. – Vol. 64 (10). – P. 3217-3227.
The rate of convergence of Hurst index estimate for the stochastic differential equation.
Stochastic Processes and Their Applications. – 2012. – Vol. 122 (11). – P. 3718-3739.

Mishura Y., Valkeila E.
An extension of the Lévy characterization to fractional Brownian motion.
Annals of Probability. – 2011. – Vol. 39 (2). – P. 439-470.

Mishura Y., Melnikov A.
On pricing and hedging in financial markets with long-range dependence.
Mathematics and Financial Economics. – 2011. – Vol. 5 (1). – P. 29-46.

Contacts

Homepage: http://probability.univ.kiev.ua/index.php?page=userinfo&person=myus&lan=en


myus@univ.kiev.ua