Advertisement

Introduction to Stochastic Calculus

  • Rajeeva L. Karandikar
  • B. V. Rao

Part of the Indian Statistical Institute Series book series (INSIS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Rajeeva L. Karandikar, B. V. Rao
    Pages 1-33
  3. Rajeeva L. Karandikar, B. V. Rao
    Pages 35-63
  4. Rajeeva L. Karandikar, B. V. Rao
    Pages 65-87
  5. Rajeeva L. Karandikar, B. V. Rao
    Pages 89-160
  6. Rajeeva L. Karandikar, B. V. Rao
    Pages 161-213
  7. Rajeeva L. Karandikar, B. V. Rao
    Pages 215-220
  8. Rajeeva L. Karandikar, B. V. Rao
    Pages 221-249
  9. Rajeeva L. Karandikar, B. V. Rao
    Pages 251-302
  10. Rajeeva L. Karandikar, B. V. Rao
    Pages 303-320
  11. Rajeeva L. Karandikar, B. V. Rao
    Pages 321-360
  12. Rajeeva L. Karandikar, B. V. Rao
    Pages 361-381
  13. Rajeeva L. Karandikar, B. V. Rao
    Pages 383-410
  14. Rajeeva L. Karandikar, B. V. Rao
    Pages 411-434
  15. Back Matter
    Pages 435-441

About this book

Introduction

This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the topic.

Keywords

Stochastic Calculus Martingale Convergence Theorem Continuous Time Process The Ito Integral Stochastic Integration Semimartingales

Authors and affiliations

  • Rajeeva L. Karandikar
    • 1
  • B. V. Rao
    • 2
  1. 1.Chennai Mathematical InstituteSiruseriIndia
  2. 2.Chennai Mathematical InstituteSiruseriIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-8318-1
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-10-8317-4
  • Online ISBN 978-981-10-8318-1
  • Series Print ISSN 2523-3114
  • Series Online ISSN 2523-3122
  • Buy this book on publisher's site
Industry Sectors
Pharma
Materials & Steel
Biotechnology
Finance, Business & Banking
Electronics
Telecommunications
Aerospace
Oil, Gas & Geosciences
Engineering