Introduction to stochastic calculus with application software#
In 2006, he moved to Cranes Software International Limited, where he was executive vice president for analytics until 2010. He returned to the Indian Statistical Institute, New Delhi, India, in 1984. He spent two years as a visiting professor at the University of North Carolina, Chapel Hill, USA, and worked with Prof. He received his MStat and PhD from the Indian Statistical Institute, Kolkata, India, in 19, respectively. Karandikar is a fellow of the Indian Academy of Sciences, Bengaluru, India, and the Indian National Science Academy, New Delhi, India. An Indian mathematician, statistician and psephologist, Prof. Rajeeva Laxman Karandikar has been professor and director of Chennai Mathematical Institute, Tamil Nadu, India, since 2010. 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. 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. Later, by using Metivier–Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. 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. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. 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. For mathematicians, this book can be used as a first text on stochastic calculus or as a companion to more rigorous texts by a way of examples and exercises.This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance.
The book covers models in mathematical finance, biology and engineering. Using such structure, the text will provide a mathematically literate reader with rapid introduction to the subject and its advanced applications. It contains many solved examples and exercises making it suitable for self study.In the book many of the concepts are introduced through worked-out examples, eventually leading to a complete, rigorous statement of the general result, and either a complete proof, a partial proof or a reference.
It is also suitable for researchers to gain working knowledge of the subject. It may be used as a textbook by graduate and advanced undergraduate students in stochastic processes, financial mathematics and engineering. Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition.This book aims to present the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. In finance, the stochastic calculus is applied to pricing options by no arbitrage. It also gives its main applications in finance, biology and engineering. This book presents a concise and rigorous treatment of stochastic calculus.
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