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Information × Registration Number 0221U105319, 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 Yuliya S., Доктор фізико-математичних наук Registration Date 25-06-2021 Organization Taras Shevchenko National University of Kyiv popup.description2 The object of research - random processes and fields, stochastic differential equations, models with stochastic volatility, insurance and financial markets, regression models. The purpose of the work is to develop methods for calculating option prices, to study the conditions of existence and unity and the properties of solutions of stochastic differential equations with partial derivative and fractional Brownian field, hyperbolic and parabolic equations with random factors and differential equations with fractional operators, development new methods for estimating the parameters of radiation risk models, development of accurate and approximate methods for estimating insurance and financial risks. Research methods - analytical methods of probability theory and mathematical statistics, methods of stochastic analysis, statistical modeling of random processes and fields, optimization theories and numerical methods. The main research results obtained in the work: Solved the problem of pricing associated with payments of polynomial growth, which may have gaps of the 1st kind, while the dynamics of asset prices is described by the Black-Scholes model, characterized by stochastic volatility controlled by fractional the Ornstein – Uhlenbeck process. Three approaches have been developed and quantified. The existence and uniqueness of a weak solution of a stochastic differential equation with partial derivatives containing a fractional Brownian field is proved and its properties are investigated. In particular, the smoothness of trajectories is established and the order of growth at infinity is estimated. The Cauchy problem for a stochastic differential equation of parabolic type with random Levy noise, which is white in space and fractional in time, is considered. The existence of a solution of the Cauchy problem in the space of functions integrated in power p is proved. Product Description popup.authors Bondarchuk Iryna M. Golomoziy Vitaliy V. Kukush Aleksandr G. Moklyachuk Мyhaylo P. Rozora Iryna Vasylivna Sakhno Liudmyla M. Shevchenko Georgy M. Shkliar Sergiy V. popup.nrat_date 2021-06-25 Close