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Brownian motion, martingales, and stochastic calculus /[edited by] Jean-Francois Le Gall.
Switzerland : Springer, 2016
282 pages. : illustrations
Ký hiệu phân loại (DDC): 519.23
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô?s formula, the optional stopping theorem and Girsanov?s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.
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Introductory course on financial mathematics / M. V. Tretyakov.
London :Imperial College Press,2013.
x, 266 pages. : ill. ;24 cm.
Ký hiệu phân loại (DDC): 332
This book is an elementary introduction to the basic concepts of financial mathematics with a central focus on discrete models and an aim to demonstrate simple, but widely used, financial derivatives for managing market risks. Only a basic knowledge of probability, real analysis, ordinary differential equations, linear algebra and some common sense are required to understand the concepts considered in this book.Financial mathematics is an application of advanced mathematical and statistical methods to financial management and markets, with a main objective of quantifying and hedging risks. Since the book aims to present the basics of financial mathematics to the reader, only essential elements of probability and stochastic analysis are given to explain ideas concerning derivative pricing and hedging. To keep the reader intrigued and motivated, the book has a 'sandwich' structure: probability and stochastics are given in situ where mathematics can be readily illustrated by application to finance.The first part of the book introduces one of the main principles in finance -- 'no arbitrage pricing'. It also introduces main financial instruments such as forward and futures contracts, bonds and swaps, and options. The second part deals with pricing and hedging of European- and American-type options in the discrete-time setting. In addition, the concept of complete and incomplete markets is discussed. Elementary probability is briefly revised and discrete-time discrete-space stochastic processes used in financial modelling are considered. The third part introduces the Wiener process, Ito integrals and stochastic differential equations, but its main focus is the famous Black-Scholes formula for pricing European options. Some guidance for further study within this exciting and rapidly changing field is given in the concluding chapter. There are approximately 100 exercises interspersed throughout the book, and solutions for most problems are provided in the appendices.
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Stochastic models of tumor latency and their biostatistical applications / Andrej Yu Yakovlev, A. D. Tsodikov, B. Asselain
Singapore : World Scientific, 1996.
xvi, 269 pages. : illustrations ; 23 cm.
Ký hiệu phân loại (DDC): 614.5
This research monograph discusses newly developed mathematical methods and models that provide biologically meaningful inferences from cancer latency data generated by discrete surveillance studies. discrete and next. Methods for designing optimal strategies in cancer surveillance are presented for the first time systematically in this book. It provides novel approaches to stochastic characterization of tumor latency, uses biologically based models to make statistical inferences from data on tumor recurrence, and also discusses on methods of statistical analysis of data from discrete monitoring strategies.
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