Advertisement

Stochastic Calculus

An Introduction Through Theory and Exercises

  • Paolo Baldi

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Paolo Baldi
    Pages 1-29
  3. Paolo Baldi
    Pages 31-44
  4. Paolo Baldi
    Pages 45-84
  5. Paolo Baldi
    Pages 85-107
  6. Paolo Baldi
    Pages 109-150
  7. Paolo Baldi
    Pages 151-179
  8. Paolo Baldi
    Pages 181-213
  9. Paolo Baldi
    Pages 215-254
  10. Paolo Baldi
    Pages 255-303
  11. Paolo Baldi
    Pages 305-339
  12. Paolo Baldi
    Pages 341-364
  13. Paolo Baldi
    Pages 365-394
  14. Paolo Baldi
    Pages 395-435
  15. Back Matter
    Pages 437-627

About this book

Introduction

This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions.

After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used.

Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical statements and rigorous proofs, this book is completely self-contained and suitable for lecture courses as well as self-study.

Keywords

stochastic calculus stochastic calculus exercises probability elements stochastic processes Brownian motion Brownian motion exercises conditional probability martingales martingales exercises Markov processes stochastic integral stochastic differential equations stochastic differential equations exercises PDE problems SDE approximation stochastic differential equation approximation stochastic calculus financial models stochastic calculus finance numerical simulation 60H10, 60H05, 60H30, 60G42, 60G44

Authors and affiliations

  • Paolo Baldi
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-62226-2
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-62225-5
  • Online ISBN 978-3-319-62226-2
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site