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Introduction to Stochastic Calculus: Indian Statistical Institute Series

Autor Rajeeva L. Karandikar, B. V. Rao
en Limba Engleză Hardback – 15 iun 2018
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.
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Specificații

ISBN-13: 9789811083174
ISBN-10: 9811083177
Pagini: 375
Ilustrații: XIII, 441 p.
Dimensiuni: 155 x 235 x 31 mm
Greutate: 0.81 kg
Ediția:1st ed. 2018
Editura: Springer Nature Singapore
Colecția Springer
Seria Indian Statistical Institute Series

Locul publicării:Singapore, Singapore

Cuprins

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.

Recenzii

“The style is compact and clear. The presentation is well complemented by a large number of useful remarks and exercises. Graduate students attending university courses in modern probability theory and its applications can benefit a lot from working with this book. There are good reasons to expect that the book will be met positively by students, university teachers and young researchers.” (Jordan M. Stoyanov, zbMATH 1434.60003, 2020)

Notă biografică

Rajeeva Laxman Karandikar has been professor and director of Chennai Mathematical Institute, Tamil Nadu, India, since 2010. An Indian mathematician, statistician and psephologist, Prof. Karandikar is a fellow of the Indian Academy of Sciences, Bengaluru, India, and the Indian National Science Academy, New Delhi, India. He received his MStat and PhD from the Indian Statistical Institute, Kolkata, India, in 1978 and 1981, respectively. He spent two years as a visiting professor at the University of North Carolina, Chapel Hill, USA, and worked with Prof. Gopinath Kallianpur. He returned to the Indian Statistical Institute, New Delhi, India, in 1984. In 2006, he moved to Cranes Software International Limited, where he was executive vice president for analytics until 2010. His research interests include stochastic calculus, filtering theory, option pricing theory, psephology in the context of Indian elections and cryptography, among others.

B.V. Rao is an adjunct professor at Chennai Mathematical Institute, Tamil Nadu, India. He received his MSc degree in Statistics from Osmania University, Hyderabad, India, in 1965 and the doctoral degree from the Indian Statistical Institute, Kolkata, India, in 1970. His research interests include descriptive set theory, analysis, probability theory and stochastic calculus. He was a professor and later a distinguished scientist at the Indian Statistical Institute, Kolkata. Generations of Indian probabilists have benefitted from his teaching, where he taught from 1973 till 2009.

Textul de pe ultima copertă

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.

Caracteristici

Discusses quadratic variation of a square integrable martingale, pathwise formulae for the stochastic integral, Emery topology, and sigma-martingales Uses the technique of random time change to study the solution of a stochastic differential equation (SDE) driven by continuous semi-martingales Studies the predictable increasing process to introduce predictable stopping times and to prove the Doob–Meyer decomposition theorem Gives an extensive treatment of representation of martingales as stochastic integrals Is useful for a two-semester graduate-level course on measure-theoretic probability