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This book is among the first concise presentations of the set-valued stochastic integration theory as well as its natural applications, as well as the first to contain complex approach theory of set-valued stochastic integrals. Taking particular consideration of set-valued Itô , set-valued stochastic Lebesgue, and stochastic Aumann integrals, the volume is divided into nine parts. It begins with preliminaries of mathematical methods that are then applied in later chapters containing the main results and some of their applications, and contains many new problems. Methods applied in the book are mainly based on functional analysis, theory of probability processes, and theory of set-valued mappings.
The volume will appeal to students of mathematics, economics, and engineering, as well as to mathematics professionals interested in applications of the theory of set-valued stochastic integrals.
List of contents
Preface.- List of Symbols.- 1. Preliminaries.- 2. Multifunctions.- 3. Decomposable Subsets of the Space Lp(T,F,Mu, X).- 4. Aumann Stochastic Integrals.- 5. Set-Valued Ito Integrals.- 6. Stochastic Differential Inclusions.- 7. Set-Valued Stochastic Differential Equations and Inclusions.- 8. Stochastic Optimal Control Problems.- 9. Mathematical Finance Problems.- References.- Index.
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"The main information on bibliographical sources of the material presented in each chapter ... . The author has done a fine job. He has written a book that will be a valuable source of information to researchers ... . The book is very interesting for experts as well as novices. It gives a new and interesting variant of the theory of stochastic integration that involves new types of arguments and insights." (Jerzy Motyl, Mathematical Reviews, March, 2022)
