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Set-Valued Stochastic Integrals and Applications

  • Book
  • © 2020

Overview

Authors:
  1. Michał Kisielewicz

    1. Faculty of Mathematics, University of Zielona Góra, Zielona Góra, Poland

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  • Functions as a self-contained volume, containing preliminaries introducing methods applied in the text
  • Presents recent and pressing issues in set-valued stochastic integrals and some of their applications
  • Contains examples of applications to financial mathematics and engineering problems

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 157)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xii
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  2. Preliminaries

    • Michał Kisielewicz
    Pages 1-59

  3. Multifunctions

    • Michał Kisielewicz
    Pages 61-79

  4. Decomposable Subsets of \({\mathbb {L}}^p(T,\mathcal {F},\mu ,X)\)

    • Michał Kisielewicz
    Pages 81-106

  5. Aumann Stochastic Integrals

    • Michał Kisielewicz
    Pages 107-139

  6. Itô Set-Valued Integrals

    • Michał Kisielewicz
    Pages 141-193

  7. Stochastic Differential Inclusions

    • Michał Kisielewicz
    Pages 195-210

  8. Set-Valued Stochastic Equations and Inclusions

    • Michał Kisielewicz
    Pages 211-247

  9. Stochastic Optimal Control Problems

    • Michał Kisielewicz
    Pages 249-258

  10. Mathematical Finance Problems

    • Michał Kisielewicz
    Pages 259-274

  11. Back Matter

    Pages 275-281
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Keywords

About this book

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.





Reviews

“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)

Authors and Affiliations

  • Faculty of Mathematics, University of Zielona Góra, Zielona Góra, Poland

    Michał Kisielewicz

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