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Author : Paul Malliavin
Release : 2006-02-25
Genre : Business & Economics
Kind : eBook
Book Rating : 990/5 ( reviews)
Book Synopsis Stochastic Calculus of Variations in Mathematical Finance by : Paul Malliavin
Download or read book Stochastic Calculus of Variations in Mathematical Finance written by Paul Malliavin. This book was released on 2006-02-25. Available in PDF, EPUB and Kindle. Book excerpt: Highly esteemed author Topics covered are relevant and timely
Author : Yasushi Ishikawa
Release : 2023-07-24
Genre : Mathematics
Kind : eBook
Book Rating : 323/5 ( reviews)
Book Synopsis Stochastic Calculus of Variations by : Yasushi Ishikawa
Download or read book Stochastic Calculus of Variations written by Yasushi Ishikawa. This book was released on 2023-07-24. Available in PDF, EPUB and Kindle. Book excerpt: This book is a concise introduction to the stochastic calculus of variations for processes with jumps. The author provides many results on this topic in a self-contained way for e.g., stochastic differential equations (SDEs) with jumps. The book also contains some applications of the stochastic calculus for processes with jumps to the control theory, mathematical finance and so. This third and entirely revised edition of the work is updated to reflect the latest developments in the theory and some applications with graphics.
Author : Marek Capiński
Release : 2012-08-23
Genre : Business & Economics
Kind : eBook
Book Rating : 409/5 ( reviews)
Book Synopsis Stochastic Calculus for Finance by : Marek Capiński
Download or read book Stochastic Calculus for Finance written by Marek Capiński. This book was released on 2012-08-23. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses specifically on the key results in stochastic processes that have become essential for finance practitioners to understand. The authors study the Wiener process and Itô integrals in some detail, with a focus on results needed for the Black–Scholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Itô formula (proved in detail) become the centrepiece, both for theory and applications, and to provide concrete examples of stochastic differential equations used in finance. Finally, proofs of the existence, uniqueness and the Markov property of solutions of (general) stochastic equations complete the book. Using careful exposition and detailed proofs, this book is a far more accessible introduction to Itô calculus than most texts. Students, practitioners and researchers will benefit from its rigorous, but unfussy, approach to technical issues. Solutions to the exercises are available online.
Author : Alexander A Gushchin
Release : 2015-08-26
Genre : Mathematics
Kind : eBook
Book Rating : 761/5 ( reviews)
Book Synopsis Stochastic Calculus for Quantitative Finance by : Alexander A Gushchin
Download or read book Stochastic Calculus for Quantitative Finance written by Alexander A Gushchin. This book was released on 2015-08-26. Available in PDF, EPUB and Kindle. Book excerpt: In 1994 and 1998 F. Delbaen and W. Schachermayer published two breakthrough papers where they proved continuous-time versions of the Fundamental Theorem of Asset Pricing. This is one of the most remarkable achievements in modern Mathematical Finance which led to intensive investigations in many applications of the arbitrage theory on a mathematically rigorous basis of stochastic calculus. Mathematical Basis for Finance: Stochastic Calculus for Finance provides detailed knowledge of all necessary attributes in stochastic calculus that are required for applications of the theory of stochastic integration in Mathematical Finance, in particular, the arbitrage theory. The exposition follows the traditions of the Strasbourg school. This book covers the general theory of stochastic processes, local martingales and processes of bounded variation, the theory of stochastic integration, definition and properties of the stochastic exponential; a part of the theory of Lévy processes. Finally, the reader gets acquainted with some facts concerning stochastic differential equations. Contains the most popular applications of the theory of stochastic integration Details necessary facts from probability and analysis which are not included in many standard university courses such as theorems on monotone classes and uniform integrability Written by experts in the field of modern mathematical finance
Author : Jai Rathod
Release : 2015-08
Genre :
Kind : eBook
Book Rating : 906/5 ( reviews)
Book Synopsis Introduction to Stochastic Analysis and Malliavin Calculus by : Jai Rathod
Download or read book Introduction to Stochastic Analysis and Malliavin Calculus written by Jai Rathod. This book was released on 2015-08. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly. The best-known stochastic process to which stochastic calculus is applied is the Wiener process, the Wiener process has been widely applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates. The Malliavin calculus extends the calculus of variations from functions to stochastic processes. The Malliavin calculus is also called the stochastic calculus of variations. In particular, it allows the computation of derivatives of random variables. Malliavin's ideas led to a proof that H�rmander's condition implies the existence and smoothness of a density for the solution of a stochastic differential equation; H�rmander's original proof was based on the theory of partial differential equations. The calculus has been applied to stochastic partial differential equations as well. The calculus allows integration by parts with random variables; this operation is used in mathematical finance to compute the sensitivities of financial derivatives. The calculus has applications in, for example, stochastic filtering. This book emphasizes on differential stochastic equations and Malliavin calculus.
