
POSITION
Head of the Department of Probability, Statistics and Actuarial Mathematics
WORK EXPERIENCE
1976–1980
Assistant Professor, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
1980–1986
Lecturer, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
1986–1991
Associated Professor, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
1991–2003
Professor, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
2003–Present
Head of the Department of Probability, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Kyiv (Ukraine)
EDUCATION AND TRAINING
1975
BSc + MSc, Kyiv State University, Kyiv (Ukraine)
1978
PhD, Kyiv State University, Kyiv (Ukraine)
1990
DSc (Habilitation), Institute of Mathematics, 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
Yuliya Mishura is the supervisor of the scientific project titled “Exact formulas, estimates, asymptotic properties and statistical analysis of complex evolutionary systems with many degrees of freedom”. 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 15 researchers and 8 PhD students:
7 DSc: V.Knopova, M.Maiboroda, M.Moklyachuk, K.Ralchenko,
L.Sakhno, G.Shevchenko, R.Yamnenko
8 PhD: I.Bodnarchuk, O.Borysenko, O.Chernova, V.Golomozi,
O.Ragulina, S.Shklyar, V.Zubchenko, T.Yanevych
8 PhD students: D.Avetisian, O.Hopkalo, O. Kharytonova, S.Logvinenko,
V.Miroshnichenko, G.Navara, M.Yakovliev, G.Zhelezniak
We maintain close collaboration with universities of Vilnius, Oslo, Liverpool, Napoli, Dresden and others.
Projects:
20002002  INTAS Grant 9900016 “Stochastic Processes and stochastic analysis with statistical applications”, coordinator of the Ukrainian group,
20042008  TEMPUSTACIS IBJEP250542004 “Educational Courses for Actuaries and Financial Analysists”, leader of the team of Kyiv National University,
20032006  NATO Grant PST.CLG.980408 “Fractional calculus and related stochastic processes and equations”,
20092012  Research European project Multifractionality, Grant Agreement N.230804, “Multiparameter Multifractional Brownian Motion”, International Research Staff Exchange (IRSES), leader of the team of Kyiv National University.
20182020  Project STORM: “Stochastics for TimeSpace Risk Models” with University of Oslo.
20202022  Grant of State Fund for Fundamental Research of Ukraine, project “Estimation of parameters, testing of hypotheses and forecasting in actual stochastic models”, 2020.02/0026
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
Methodological and Technical Expertise
Selected Publications
 G. Kulinich, S. Kushnirenko, Yu. Mishura. "Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations". Vol.9, Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics, 248 p.  2020.

O. Banna, Yu. Mishura, K. Ralchenko, S. Shklyar. "Fractional Brownian Motion. Approximations and Projections". WileyISTE, 288 p.  2019.

Yu. Mishura, M. Zili. "Stochastic Analysis of Mixed Fractional Gaussian Processes". ISTE Press  Elsevier, 210 p.  2018.

K. Kubilius, Yu. Mishura, K. Ralchenko. "Parameter Estimation in Fractional Diffusion Models".
Bocconi & Springer Series, 380 p.  2017.

Yu. Mishura. "Stochastic calculus for fractional Brownian motion and related processes". Vol. 1929 of Lecture Notes in Mathematics, Springer Science & Business Media, 410 p.  2008.

J. Eisenberg, Yu. Mishura. "Optimising Dividends and Consumption Under an Exponential CIR as a Discount Factor".
Mathematical Methods of Operations Research, Vol. 92, pp. 285309.  2020.

Yu. Mishura, K. Ralchenko, S. Shklyar "General Conditions of Weak Convergence of DiscreteTime Multiplicative Scheme to Asset Price with Memory ". Risks, Vol. 8, Iss.1, pp. 129.  2020.

G. Ascione, Yu. Mishura, E. Pirozzi. "TimeChanged Fractional OrnsteinUhlenbeck Process". Fractional Calculus and Applied Analysis, Vol. 23, Iss.2, pp. 450 483.  2020.

Yu. Kondratiev, Yu. Mishura, G. Shevchenko. " Limit theorems for additive functionals of continuous time random walks". Proceedings of the Royal Society of Edinburgh Section A: Mathematics, pp. 122.  2020.

P. Guasoni, Yu. Mishura, M. Rasonyi. "HighFrequency Trading with Fractional Brownian Motion". Finance and Stochastics.  2020.

V. Bezborodov, L. Di Persio, Yu. Mishura "Option Pricing with Fractional Stochastic Volatility and Discontinuous Payoff Function of Polynomial Growth". Methodology and Computing in Applied Probability. Vol.21, Iss.1, pp. 331366.  2019.

Yu. Mishura, A. Schied. "On (signed) Takagi–Landsberg functions: pth variation, maximum, and modulus of continuity". Journal of Mathematical Analysis and Applications, Vol. 473, Iss.1, 258272.  2019.
Contacts
Homepage: http://probability.univ.kiev.ua/index.php?page=userinfo&person=myus&lan=en
myus@univ.kiev.ua
