000			03475nam a22003617a 4500
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005			20250215154158.0
008			250215b |||||||| |||| 00| 0 hin d
020			_a9783662647103
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a519.21 _bRUS-S
100	1		_aRüschendorf, Ludger
245			_aStochastic processes and financial mathematics
260			_aBerlin, Heidelberg : _bSpringer Berlin / Heidelberg, _c2023.
300			_aix, 304 pages : _billustrations (1 b/w illustrations)
490			_aMathematics study resources ; _vvolume 1
504			_aIncludes bibliographical references and index.
520			_aThe book provides an introduction to advanced topics in stochastic processes and related stochastic analysis, and combines them with a sound presentation of the fundamentals of financial mathematics. It is wide-ranging in content, while at the same time placing much emphasis on good readability, motivation, and explanation of the issues covered. Financial mathematical topics are first introduced in the context of discrete time processes and then transferred to continuous-time models. The basic construction of the stochastic integral and the associated martingale theory provide fundamental methods of the theory of stochastic processes for the construction of suitable stochastic models of financial mathematics, e.g. using stochastic differential equations. Central results of stochastic analysis such as the Itô formula, Girsanov's theorem and martingale representation theorems are of fundamental importance in financial mathematics, e.g. for the risk-neutral valuation formula (Black-Scholes formula) or the question of the hedgeability of options and the completeness of market models. Chapters on the valuation of options in complete and incomplete markets and on the determination of optimal hedging strategies conclude the range of topics. Advanced knowledge of probability theory is assumed, in particular of discrete-time processes (martingales, Markov chains) and continuous-time processes (Brownian motion, Lévy processes, processes with independent increments, Markov processes). The book is thus suitable for advanced students as a companion reading and for instructors as a basis for their own courses. This book is a translation of the original German 1st edition Stochastische Prozesse und Finanzmathematik by Ludger Rüschendorf, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com) and in a subsequent editing, improved by the author. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
650		0	_aStochastic processes
650		0	_aBusiness mathematics
650		0	_aFinancial mathematics
650		0	_aSkorohods embedding theorem
650		0	_aDonsker theorem
650		0	_aStochastic integral
650		0	_aStochastic analysis
650		0	_aOption pricing
650		0	_aBlack-Scholes model
650		0	_aPortfolio optimization
650		0	_aUtility optimization
856			_3Table of content _uhttps://link.springer.com/content/pdf/bfm:978-3-662-64711-0/1
856			_3Reviews _uhttps://www.goodreads.com/book/show/211918505-stochastic-processes-and-financial-mathematics?ref=nav_sb_ss_1_13#CommunityReviews
942			_2udc _cBK
999			_c35669 _d35669