Yuliya Mishura's Books

Fractional Brownian Motion

Approximations and Projections

By: Oksana Banna,Yuliya Mishura,Kostiantyn Ralchenko,Sergiy Shklyar

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Fractional Brownian Motion

Approximations and Projections

By: Oksana Banna,Yuliya Mishura,Kostiantyn Ralchenko,Sergiy Shklyar

This monograph studies the relationships between fractional Brownian motion (fBm) and other processes of more simple form. In particular, this book solves the problem of the projection of fBm onto the space of Gaussian martingales that can be represented as Wiener integrals with respect to a Wiener process. It is proved that there exists a unique martingale closest to fBm in the uniform integral norm. Numerical results concerning the approximation problem are given. The upper bounds of distances from fBm to the different subspaces of Gaussian martingales are evaluated and the numerical calculations are involved. The approximations of fBm by a uniformly convergent series of Lebesgue integrals, semimartingales and absolutely continuous processes are presented. As auxiliary but interesting results, the bounds from below and from above for the coefficient appearing in the representation of fBm via the Wiener process are established and some new inequalities for Gamma functions, and even for trigonometric functions, are obtained.

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Page Count

245

Publisher

John Wiley & Sons

Published Date

ISBN 10

1119610338

ISBN 13

9781119610335

Stochastic Calculus for Fractional Brownian Motion and Related Processes

By: Yuliya Mishura

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Stochastic Calculus for Fractional Brownian Motion and Related Processes

By: Yuliya Mishura

This volume examines the theory of fractional Brownian motion and other long-memory processes. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. It proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.

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Page Count

411

Publisher

Springer

Published Date

ISBN 10

3540758739

ISBN 13

9783540758730

Theory and Statistical Applications of Stochastic Processes

By: Yuliya Mishura,Georgiy Shevchenko

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Theory and Statistical Applications of Stochastic Processes

By: Yuliya Mishura,Georgiy Shevchenko

This book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent increments, Gaussian processes, martingales, Markov properties, continuity and related properties of trajectories with contemporary subjects: integration with respect to Gaussian processes, Itȏ integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.

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Page Count

400

Publisher

John Wiley & Sons

Published Date

ISBN 10

1786300508

ISBN 13

9781786300508

Financial Mathematics

By: Yuliya Mishura

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Financial Mathematics

By: Yuliya Mishura

Finance Mathematics is devoted to financial markets both with discrete and continuous time, exploring how to make the transition from discrete to continuous time in option pricing. This book features a detailed dynamic model of financial markets with discrete time, for application in real-world environments, along with Martingale measures and martingale criterion and the proven absence of arbitrage. With a focus on portfolio optimization, fair pricing, investment risk, and self-finance, the authors provide numerical methods for solutions and practical financial models, enabling you to solve problems both from mathematical and from financial point of view. - Calculations of Lower and upper prices, featuring practical examples - The simplest functional limit theorem proved for transition from discrete to continuous time - Learn how to optimize portfolio in the presence of risk factors

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Page Count

196

Publisher

Elsevier

Published Date

ISBN 10

0081004885

ISBN 13

9780081004883

Stochastic Analysis of Mixed Fractional Gaussian Processes

By: Yuliya Mishura,Mounir Zili

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Stochastic Analysis of Mixed Fractional Gaussian Processes

By: Yuliya Mishura,Mounir Zili

Stochastic Analysis of Mixed Fractional Gaussian Processes presents the main tools necessary to characterize Gaussian processes. The book focuses on the particular case of the linear combination of independent fractional and sub-fractional Brownian motions with different Hurst indices. Stochastic integration with respect to these processes is considered, as is the study of the existence and uniqueness of solutions of related SDE's. Applications in finance and statistics are also explored, with each chapter supplying a number of exercises to illustrate key concepts. - Presents both mixed fractional and sub-fractional Brownian motions - Provides an accessible description for mixed fractional gaussian processes that is ideal for Master's and PhD students - Includes different Hurst indices

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Page Count

212

Publisher

Elsevier

Published Date

ISBN 10

0081023634

ISBN 13

9780081023631

Stochastic Calculus for Fractional Brownian Motion and Related Processes

By: Yuliya Mishura,I︠U︡lii︠a︡ S. Mishura

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Stochastic Calculus for Fractional Brownian Motion and Related Processes

By: Yuliya Mishura,I︠U︡lii︠a︡ S. Mishura

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411

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540758720

ISBN 13

9783540758723

Ruin Probabilities

Smoothness, Bounds, Supermartingale Approach

By: Yuliya Mishura,Olena Ragulina

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Ruin Probabilities

Smoothness, Bounds, Supermartingale Approach

By: Yuliya Mishura,Olena Ragulina

Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach deals with continuous-time risk models and covers several aspects of risk theory. The first of them is the smoothness of the survival probabilities. In particular, the book provides a detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities for different risk models. Next, it gives some possible applications of the results concerning the smoothness of the survival probabilities. Additionally, the book introduces the supermartingale approach, which generalizes the martingale one introduced by Gerber, to get upper exponential bounds for the infinite-horizon ruin probabilities in some generalizations of the classical risk model with risky investments. - Provides new original results - Detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities, as well as possible applications of these results - An excellent supplement to current textbooks and monographs in risk theory - Contains a comprehensive list of useful references

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Page Count

278

Publisher

Elsevier

Published Date

ISBN 10

0081020988

ISBN 13

9780081020982

Theory and Statistical Applications of Stochastic Processes

By: Yuliya Mishura,Georgiy Shevchenko

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Theory and Statistical Applications of Stochastic Processes

By: Yuliya Mishura,Georgiy Shevchenko

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Page Count

400

Publisher

John Wiley & Sons

Published Date

ISBN 10

1786300508

ISBN 13

9781786300508

Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations

By: Grigorij Kulinich,Svitlana Kushnirenko,Yuliya Mishura

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Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations

By: Grigorij Kulinich,Svitlana Kushnirenko,Yuliya Mishura

This book is devoted to unstable solutions of stochastic differential equations (SDEs). Despite the huge interest in the theory of SDEs, this book is the first to present a systematic study of the instability and asymptotic behavior of the corresponding unstable stochastic systems. The limit theorems contained in the book are not merely of purely mathematical value; rather, they also have practical value. Instability or violations of stability are noted in many phenomena, and the authors attempt to apply mathematical and stochastic methods to deal with them. The main goals include exploration of Brownian motion in environments with anomalies and study of the motion of the Brownian particle in layered media. A fairly wide class of continuous Markov processes is obtained in the limit. It includes Markov processes with discontinuous transition densities, processes that are not solutions of any Itô's SDEs, and the Bessel diffusion process. The book is self-contained, with presentation of definitions and auxiliary results in an Appendix. It will be of value for specialists in stochastic analysis and SDEs, as well as for researchers in other fields who deal with unstable systems and practitioners who apply stochastic models to describe phenomena of instability.

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Page Count

249

Publisher

Springer Nature

Published Date

ISBN 10

3030412911

ISBN 13

9783030412913

Fractional Brownian Motion

Approximations and Projections

By: Oksana Banna,Yuliya Mishura,Kostiantyn Ralchenko,Sergiy Shklyar

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Fractional Brownian Motion

Approximations and Projections

By: Oksana Banna,Yuliya Mishura,Kostiantyn Ralchenko,Sergiy Shklyar

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Page Count

245

Publisher

John Wiley & Sons

Published Date

ISBN 10

1119610338

ISBN 13

9781119610335

Theory of Stochastic Processes

With Applications to Financial Mathematics and Risk Theory

By: Dmytro Gusak,Alexander Kukush,Alexey Kulik,Yuliya Mishura,Andrey Pilipenko

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Theory of Stochastic Processes

With Applications to Financial Mathematics and Risk Theory

By: Dmytro Gusak,Alexander Kukush,Alexey Kulik,Yuliya Mishura,Andrey Pilipenko

Providing the necessary materials within a theoretical framework, this volume presents stochastic principles and processes, and related areas. Over 1000 exercises illustrate the concepts discussed, including modern approaches to sample paths and optimal stopping.

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Page Count

379

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387878629

ISBN 13

9780387878621

Parameter Estimation in Fractional Diffusion Models

By: Kęstutis Kubilius,Yuliya Mishura,Kostiantyn Ralchenko

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Parameter Estimation in Fractional Diffusion Models

By: Kęstutis Kubilius,Yuliya Mishura,Kostiantyn Ralchenko

This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.

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Page Count

403

Publisher

Springer

Published Date

ISBN 10

3319710303

ISBN 13

9783319710303

Discrete-Time Approximations and Limit Theorems

In Applications to Financial Markets

By: Yuliya Mishura,Kostiantyn Ralchenko

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Discrete-Time Approximations and Limit Theorems

In Applications to Financial Markets

By: Yuliya Mishura,Kostiantyn Ralchenko

Financial market modeling is a prime example of a real-life application of probability theory and stochastics. This authoritative book discusses the discrete-time approximation and other qualitative properties of models of financial markets, like the Black-Scholes model and its generalizations, offering in this way rigorous insights on one of the most interesting applications of mathematics nowadays.

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Page Count

390

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110654245

ISBN 13

9783110654240

Book's by Yuliya Mishura

Fractional Brownian Motion

Fractional Brownian Motion

Stochastic Calculus for Fractional Brownian Motion and Related Processes

Stochastic Calculus for Fractional Brownian Motion and Related Processes

Theory and Statistical Applications of Stochastic Processes

Theory and Statistical Applications of Stochastic Processes

Financial Mathematics

Financial Mathematics

Stochastic Analysis of Mixed Fractional Gaussian Processes

Stochastic Analysis of Mixed Fractional Gaussian Processes

Stochastic Calculus for Fractional Brownian Motion and Related Processes

Stochastic Calculus for Fractional Brownian Motion and Related Processes

Ruin Probabilities

Ruin Probabilities

Theory and Statistical Applications of Stochastic Processes

Theory and Statistical Applications of Stochastic Processes

Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations

Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations

Fractional Brownian Motion

Fractional Brownian Motion

Theory of Stochastic Processes

Theory of Stochastic Processes

Parameter Estimation in Fractional Diffusion Models

Parameter Estimation in Fractional Diffusion Models

Discrete-Time Approximations and Limit Theorems

Discrete-Time Approximations and Limit Theorems

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