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


  1. Oksana Banna, Yuliya Mishura, Kostiantyn Ralchenko, Sergiy Shklyar "Fractional Brownian Motion. Approximations and Projections". Wiley-ISTE, 288 p. - 2019 
  2. Yu. Mishura, M. Zili "Stochastic Analysis of Mixed Fractional Gaussian Processes". ISTE Press - Elsevier, 210 p. - 2018 
  3. K. Kubilius, Yu. Mishura, K. Ralchenko “Parameter Estimation in Fractional Diffusion Models “. Bocconi & Springer Series, 380 p. – 2017
  4. Mishura Y., Ragulina O. Ruin Probabilities. Smoothness, Bounds, Supermartingale Approach.” Elsevier, ISTE Press, 2016. – 276 p.
  5. Viktor Bezborodov, Luca Di Persio, Yuliya Mishura "Option Pricing with Fractional Stochastic Volatility and Discontinuous Payoff Function of Polynomial Growth". Methodology and Computing in Applied Probability https://doi.org/10.1007/s11009-018-9650-3, Vol.21, Iss.1 pp. 331 - 366, - 2019
  6. Yu. Mishura, Al. Schied "On (signed) Takagi–Landsberg functions: pth variation, maximum, and modulus of continuity". Journal of Mathematical Analysis and Applications, Vol.473, Iss.1 pp. 258 - 272, - 2019
  7. Yuliya Mishura, Anton Yurchenko-Tytarenko "Fractional Cox–Ingersoll–Ross process with small Hurst indices". Modern Stochastics: Theory and Applications, Vol.6, Iss.1 pp. 13 - 39, - 2019
  8. Vitalii Makogin and Yuliya Mishura "Gaussian multi-self-similar random fields with distinct stationary properties of their rectangular increments". Stochastic Models, https://doi.org/10.1080/15326349.2019.1610664, Vol.35, Iss.4 pp. 391 - 428, - 2019
  9. Yu. Mushura, S. Shklyar "Distance between the fractional Brownian motion and the space of adapted Gaussian martingales". Nonlinear Analysis: Modelling and Control, Vol.24, Iss.4 pp. 639 - 657, - 2019
  10. Vitalii Makogin and Yuliya Mishura "Small deviations for mixed fractional Brownian motion with trend and with Hurst index H > 1/2". Stochastics, pp. 1 - 15, - 2019
  11. Giacomo Ascione, Yuliya Mishura and Enrica Pirozzi "Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications ". Methodology and Computing in Applied Probability, https://doi.org/10.1007/s11009-019-09748-y, - 2019

Contacts

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


myus@univ.kiev.ua