Brownian Motion and Stochastic Calculus

Author: Ioannis Karatzas
Publisher: Springer
ISBN: 9781461209492
Release Date: 2014-03-27
Genre: Mathematics

A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.


Author: Achim Klenke
Publisher: Springer-Verlag
ISBN: 9783540334149
Release Date: 2006-06-09
Genre: Mathematics

Dieses Lehrbuch bietet eine umfassende moderne Einführung in die wichtigsten Gebiete der Wahrscheinlichkeitstheorie und ihre maßtheoretischen Grundlagen. Themenschwerpunkte sind u.a.: Maß- und Integrationstheorie, Grenzwertsätze für Summen von Zufallsvariablen, Martingale oder Perkolation. Über 200 Übungsaufgaben und zahlreiche Abbildungen runden die Darstellung ab. Breite und Auswahl der Themen sind einmalig in der deutschsprachigen Literatur.

Mathematik in der Praxis

Author: Achim Bachem
Publisher: Springer-Verlag
ISBN: 9783642797637
Release Date: 2013-03-12
Genre: Mathematics

Wie aufregend Mathematik im Spannungsfeld zwischen Theorie und Praxis sein kann, zeigt dieses Buch. Es beschreibt interessant und allgemeinverständlich die konkreten Anwendungen mathematischer Forschung in unserem Alltag.

Markov Processes Feller Semigroups and Evolution Equations

Author: J. A. van Casteren
Publisher: World Scientific
ISBN: 9789814322188
Release Date: 2011
Genre: Mathematics

The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.

Stochastic Processes and Applications

Author: Sergei Silvestrov
Publisher: Springer
ISBN: 9783030028251
Release Date: 2018-12-05
Genre: Mathematics

This book highlights the latest advances in stochastic processes, probability theory, mathematical statistics, engineering mathematics and algebraic structures, focusing on mathematical models, structures, concepts, problems and computational methods and algorithms important in modern technology, engineering and natural sciences applications. It comprises selected, high-quality, refereed contributions from various large research communities in modern stochastic processes, algebraic structures and their interplay and applications. The chapters cover both theory and applications, illustrated by numerous figures, schemes, algorithms, tables and research results to help readers understand the material and develop new mathematical methods, concepts and computing applications in the future. Presenting new methods and results, reviews of cutting-edge research, and open problems and directions for future research, the book serves as a source of inspiration for a broad spectrum of researchers and research students in probability theory and mathematical statistics, applied algebraic structures, applied mathematics and other areas of mathematics and applications of mathematics. The book is based on selected contributions presented at the International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications” (SPAS2017) to mark Professor Dmitrii Silvestrov’s 70th birthday and his 50 years of fruitful service to mathematics, education and international cooperation, which was held at Mälardalen University in Västerås and Stockholm University, Sweden, in October 2017.

Mathematical Tools for Physicists

Author: Michael Grinfeld
Publisher: John Wiley & Sons
ISBN: 9783527684274
Release Date: 2014-11-05
Genre: Science

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Wahrscheinlichkeitstheorie und Stochastische Prozesse

Author: Michael Mürmann
Publisher: Springer-Verlag
ISBN: 9783642381607
Release Date: 2013-11-22
Genre: Mathematics

Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.​

How to Implement Market Models Using VBA

Author: Francois Goossens
Publisher: John Wiley & Sons
ISBN: 9781118961988
Release Date: 2015-01-23
Genre: Business & Economics

Accessible VBA coding for complex financial modelling How to Implement Market Models Using VBA makes solving complex valuation issues accessible to any financial professional with a taste for mathematics. With a focus on the clarity of code, this practical introductory guide includes chapters on VBA fundamentals and essential mathematical techniques, helping readers master the numerical methods to build an algorithm that can be used in a wide range of pricing problems. Coverage includes general algorithms, vanilla instruments, multi-asset instruments, yield curve models, interest rate exotics, and more, guiding readers thoroughly through pricing in the capital markets area. The companion website ( features additional VBA code and algorithmic techniques, and the interactive blog provides a forum for discussion of code with programmers and financial engineers, giving readers insight into the different applications and customisations possible for even more advanced problem solving.. Financial engineers implement models from a mathematical representation of an asset's performance by building a program that performs a valuation of securities based on this asset. How to Implement Market Models Using VBA makes this technical process understandable, with well-explained algorithms, VBA code, and accessible theoretical explanations. Decide which numerical method to use in which scenario Identify the necessary building blocks of an algorithm Write clear, functional VBA code for a variety of problems Apply algorithms to different instruments and models Designed for finance professionals, this book brings more accurate modelling within reach for anyone with interest in the market. For clearer code, patient explanation, and practical instruction, How to Implement Market Models Using VBA is an essential introductory guide.

Optionsbewertung und Portfolio Optimierung

Author: Ralf Korn
Publisher: Springer-Verlag
ISBN: 9783322968883
Release Date: 2013-03-09
Genre: Mathematics

Der Erwartungswert-Varianz-Ansatz nach Markowitz - Das zeitstetige Marktmodell (Wertpapierpreise, vollständige Märkte, Ito-Integral und Ito-Formel, Variation der Konstanten, Martingaldarstellungsatz) - Das Optionsbewertungsproblem (Duplikationsprinzip, Satz von Girsanov, Darstellungssatz von Feynman und Kac) - Das Portfolio-Problem in stetiger Zeit (Martingalmethode, HJB-Gleichung, stochastische Steuerung)