Search academic texts

Information × Registration Number 0222U003381, 0119U100317 , R & D reports Title Exact formulas, estimates, asymptotic properties, and statistical analysis of complex evolutionary systems with many degrees of freedom. popup.stage_title Head Mishura Yuliia S., Доктор фізико-математичних наук Registration Date 16-03-2022 Organization Taras Shevchenko National University of Kyiv popup.description2 Object of research - random processes and fields, stochastic differential equations, stochastic volatility, insurance, financial, radiation risks, regression models. Purpose - development of the theory of fractional processes, development of the theory of diffusion models with stochastic volatility, construction of stochastic analysis for non-Gaussian random noise, study of stochastic equations modeling physical and financial processes, statistical estimation, approximation of random fields modeled by differential equations with random actuarial and financial risk measures, estimation of regression models with measurement errors, radiation risk parameters. Research methods - analytical methods of probability theory and mathematical statistics, methods of stochastic analysis, statistical modeling of random processes and fields, optimization theory and numerical methods. The main research results obtained in the work: The theory of fractional processes for modeling fast-changing stochastic volatility and new methods for calculating option prices with such volatility have been developed. Fractional processes of the Cox-Ingersoll-Ross type with small Hurst indices have been studied. A model of the financial market with rapidly changing stochastic volatility has been built, and the problem of pricing related to payments that may have gaps of the 1st kind has been solved. Colored in time and white in space random noise with heavy distribution tails is determined, integration on such random noise is built. The existence and uniqueness of a weak solution of a stochastic differential equation containing a fractional Brownian field is proved, and its properties are investigated. The Cauchy problem for a stochastic differential equation of parabolic type with random Levy noise fractional in time is investigated. Product Description popup.authors Bondarchuk Iryna M. Golomoziy Vitaliy V. Zubchenko Volodymyr P. Knopova Victoria P. Kozachenko Yuriy V. Kukush Oleksandr H. Kushnirenko Svitlana V. Moklyachuk Мyhaylo P. Ragulina Elena Yu. Ralchenko Kostiantyn V. Rozora Iryna V. Sakhno Liudmyla M. Shevchenko Georgy M. Shklyar Serhiy V. popup.nrat_date 2022-03-16 Close