Introduction to Stochastic Calculus

This book provides a comprehensive treatment of stochastic calculus, including pathwise formulae for the stochastic integral, advanced topics such as quadratic variation, Ito formula, and Emery topology, and the connection with mathematical finance. It is intended for undergraduate- and beginning graduate-level students in engineering and mathematics and is also a valuable reference resource for applied mathematicians and statisticians.

Format: Hardback
Length: 441 pages
Publication date: 15 June 2018
Publisher: Springer Verlag, Singapore

This comprehensive book delves into the realm of stochastic calculus, a branch of mathematics that finds widespread application in financial engineering and mathematical finance. Serving as the first publication to introduce pathwise formulae for the stochastic integral, it offers a straightforward yet rigorous treatment of the subject, encompassing a diverse range of advanced topics. The book explores in depth subjects such as quadratic variation, Ito formula, and Emery topology, providing readers with a deep understanding of these complex concepts. Additionally, the authors briefly touch upon continuous semi-martingales to derive growth estimates and employ the technique of random time change to study the solution of stochastic differential equations (SDEs). Subsequently, by utilizing the Metivier–Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The book also briefly touches upon the connection between the theory and mathematical finance, highlighting its significance in the field. Furthermore, it provides an extensive treatment on the representation of martingales as stochastic integrals and presents a second fundamental theorem of asset pricing. Designed for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, this book serves as an invaluable reference resource for applied mathematicians and statisticians seeking a comprehensive review of the topic.

Weight: 846g
Dimension: 242 x 170 x 31 (mm)
ISBN-13: 9789811083174
Edition number: 1st ed. 2018