04379nam 2200505 450 991068677990332120230605172005.09783662647110(electronic bk.)978366264710310.1007/978-3-662-64711-0(MiAaPQ)EBC7234196(Au-PeEL)EBL7234196(OCoLC)1376196389(DE-He213)978-3-662-64711-0(PPN)269658580(EXLCZ)992642828490004120230605d2023 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierStochastic processes and financial mathematics /Ludger Rüschendorf1st ed. 2023.Berlin, Germany :Springer,[2023]©20231 online resource (310 pages)Mathematics Study Resources,2731-3832 ;1Print version: Rüschendorf, Ludger Stochastic Processes and Financial Mathematics Berlin, Heidelberg : Springer Berlin / Heidelberg,c2023 9783662647103 Includes bibliographical references and index.Option pricing in models in discrete time -- Scorohod's embedding theorem and Donsker's theorem -- Stochastic integration -- Elements of stochastic analysis -- Option pricing in complete and incomplete markets -- Utility optimization, minimum distance martingales, and utility indiff -- Variance-minimum hedging.The 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. 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. 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. The Author Prof. Dr. Ludger Rüschendorf is professor at the University of Freiburg in the field of mathematical stochastics since 1993. Previously, he taught and conducted research at the universities of Hamburg, Aachen, Freiburg, and Münster.Mathematics Study Resources,2731-3832 ;1Social sciencesMathematicsStochastic processesSocial sciencesMathematics.Stochastic processes.605Rüschendorf Ludger0MiAaPQMiAaPQMiAaPQ9910686779903321Stochastic Processes and Financial Mathematics3088219UNINA