Introduction to Stochastic Calculus Indian Statistical Institute Series 1st Edition by Rajeeva Karandikar , Rao ISBN 9811341214 978-9811341212

Introduction to Stochastic Calculus  (Indian Statistical Institute Series) 1st Edition by Rajeeva L. Karandikar , B. V. Rao – Ebook PDF Instant Download/Delivery:9811341214 978-9811341212
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ISBN 10: 9811341214
ISBN 13: 978-9811341212
Author: Rajeeva L. Karandikar , B. V. Rao

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 addresses 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.

Introduction to Stochastic Calculus  (Indian Statistical Institute Series) 1st Table of contents:

Continuous-Time Processes

The Ito’s 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

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Rajeeva Karandikar,Rao,Stochastic Calculus,Institute Series