Introduction to Stochastic Calculus

• Main Authors: Karandikar, Rajeeva L. (Author, http://id.loc.gov/vocabulary/relators/aut), Rao, B. V. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Indian Statistical Institute Series,
• Subjects: Statistics .; Probabilities.; Statistical Theory and Methods.; Probability Theory and Stochastic Processes.

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...

Table of Contents:

• Discrete Parameter Martingales
• Continuous Time Processes
• The Ito Integral
• Stochastic Integration
• Semimartingales
• Pathwise Formula for the Stochastic Integral
• Continuous Semimartingales
• Predictable Increasing Processes
• The Davis Inequality
• Integral Representation of Martingales
• Dominating Process of a Semimartingale
• SDE driven by r.c.l.l. Semimartingales
• Girsanov Theorem.