{"title":"Yuliya Mishura","description":null,"products":[{"product_id":"stochastic-calculus-for-fractional-brownian-motion-and-related-processes-book-yuliya-mishura-9783540758723","title":"Stochastic Calculus for Fractional Brownian Motion and Related Processes","description":"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.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50059186340113,"sku":"GOR013849647","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52400594223377,"sku":"NLS9783540758723","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3540758720.jpg?v=1750773986"},{"product_id":"discrete-time-approximations-and-limit-theorems-book-yuliya-mishura-9783110652796","title":"Discrete-Time Approximations and Limit Theorems","description":"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.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51187779993873,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51187781763345,"sku":"NIN9783110652796","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52613928157457,"sku":"NLS9783110652796","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/311065279X.jpg?v=1751350388"},{"product_id":"entropies-and-fractionality-book-yuliya-mishura-9781041074786","title":"Entropies and Fractionality","description":"\u003cp\u003e\u003cstrong\u003eEntropies and Fractionality: Entropy Functionals, Small Deviations and Related Integral Equations\u003c\/strong\u003e starts with a systematization and calculation of various entropies (Shannon, Rényi, and some others) of selected absolutely continuous probability distributions. The properties of the entropies are analyzed. Subsequently, a related problem is addressed: the computation and investigation of the properties of the entropic risk measure, Entropic Value-at-Risk (EVaR).\u003c\/p\u003e\u003cp\u003eNext, the book computes and compares entropy values for the one-dimensional distributions of various fractional Gaussian processes. Special attention is then given to fractional Gaussian noise, where the authors conduct a detailed analysis of the properties and asymptotic behavior of Shannon entropy. Additionally, two alternative entropy functionals are introduced which are more suitable for analytical investigation.\u003c\/p\u003e\u003cp\u003eFurthermore, relative entropy functionals for the sum of two independent Wiener processes with drift are considered, and their minimization and maximization are explored. A similar problem is addressed for a mixed fractional Brownian motion (i.e., the sum of a Wiener process and a fractional Brownian motion) with drift. The entropy minimization problem is reduced to a Fredholm integral equation of the second kind, and its unique solvability is thoroughly investigated.\u003c\/p\u003e\u003cp\u003eIn the final part of the book, the optimization of small deviations for mixed fractional Brownian motion with trend is studied. This problem is closely related to the minimization of relative entropy functionals and is solved using similar techniques and results, which leads to the same class of integral equations. Since solving such equations is challenging due to the presence of an additional singularity in the kernel, efficient numerical methods have been developed to address this difficulty.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFeatures\u003c\/b\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eUseful both for mathematicians interested in problems related to entropy and for practitioners, especially specialists in physics, finance, and information theory\u003c\/li\u003e\n\u003cli\u003eNumerous examples and applications are provided, with rigorous proofs\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51599277588753,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":51599279292689,"sku":"NGR9781041074786","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52613868552465,"sku":"NLS9781041074786","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1041074786.jpg?v=1755598745"},{"product_id":"ruin-probabilities-book-yuliya-mishura-9781785482182","title":"Ruin Probabilities","description":"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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52123320516881,"sku":"NLS9781785482182","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781785482182.jpg?v=1757449056"},{"product_id":"parameter-estimation-in-fractional-diffusion-models-book-kostiantyn-ralchenko-9783319710297","title":"Parameter Estimation in Fractional Diffusion Models","description":"This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52124503343377,"sku":"NLS9783319710297","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319710297.jpg?v=1757456878"},{"product_id":"financial-mathematics-book-yuliya-mishura-9781785480461","title":"Financial Mathematics","description":"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.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52456494956817,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52456495612177,"sku":"NLS9781785480461","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781785480461.jpg?v=1759377514"},{"product_id":"stochastic-analysis-of-mixed-fractional-gaussian-processes-book-yuliya-mishura-9781785482458","title":"Stochastic Analysis of Mixed Fractional Gaussian Processes","description":"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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":53522412634385,"sku":"NLS9781785482458","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781785482458.jpg?v=1778458219"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-yuliya-mishura.oembed","provider":"World of Books ","version":"1.0","type":"link"}