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.
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.
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.
Author: J. A. van Casteren
Publisher: World Scientific
Release Date: 2011
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.
Author: Francois Goossens
Publisher: John Wiley & Sons
Release Date: 2015-01-23
Genre: Business & Economics
Praise for How to Implement Market Models Using VBA "This well-written book proposes a wide instructional use of Visual Basic in order to learn computational finance in more detail by covering issues and techniques useful for quant/trading jobs in investment companies. All readers, students or financial engineers, will find much to improve their thinking of VBA when applied to finance thanks to the important resource of examples. I strongly recommend this new book to accompany each step toward successful programming." —Sofiane Aboura Professor of finance, University of Paris Dauphine "This book offers the reader a unique opportunity to obtain both introductory and advanced knowledge in Finance with direct implementations in VBA. It starts with a survival kit for VBA newcomers and covers classical techniques usually studied in MSc Finance programs. However, it also presents more sophisticated approaches to these topics (among others, the HJM and Heston models), qualifying the book for both professionals and advanced students in quantitative/computational Finance. As such I would recommend this book to my students attending the Master 'Financial and Risk Engineering' or under my supervision in a PhD program, as well as to everyone willing to update or upgrade his knowledge in VBA for implementing market models in a professional environment." —Olivier Brandouy Professor of finance, University of Bordeaux and IAE/Paris Sorbonne "As financial markets have reached maturity and volumes of products have dramatically increased, the emphasis of financial research has shifted from model development to model implementation. Nowadays it is paramount to use models optimally in aspects such as development costs, transparency, controllability, etc. Their implementation is therefore as important as their all-encompassing-ness, which explains why VBA has become a tool of choice to test models and valuation tools. How to Implement Market Models Using VBA proposes a rare junction between instruments types, asset classes, models and implementation techniques - presenting its material in a clear and educational manner. It is a positive addition to an often fragmented and specialised literature. This book will be of great use in the hands of graduate students as well as on the desk of practitioners." —Dr. Vincent Gesser, CEO Kleber consulting Ltd "This book tackles a wide range of technical issues arising from the implementation of popular market models in a remarkably practical manner. The author clearly does a lot to comprehensively expose the rationale under lying pricing formulae and illustrate them with an easy to learn programming language. Practitioners wishing to strengthen their quantitative insight as well as students in finance should make the best from this book." —Yassine Makrini, quantitative analyst, J.P. Morgan
Es werden die typischen Aufgabenstellungen der zeitstetigen Modellierung von Finanzmärkten wie Optionsbewertung (insbesondere auch die Black-Scholes-Formel und zugehörige Varianten) und Portfolio-Optimierung (Bestimmen optimaler Investmentstrategien) behandelt. Die benötigten mathematischen Werkzeuge (wie z. B. Brownsche Bewegung, Martingaltheorie, Ito-Kalkül, stochastische Steuerung) werden in selbständigen Exkursen bereitgestellt. Das Buch eignet sich als Grundlage einer Vorlesung, die sich an einen Grundkurs in Stochastik anschließt. Es richtet sich an Mathematiker, Finanz- und Wirtschaftsmathematiker in Studium und Beruf und ist aufgrund seiner modularen Struktur auch für Praktiker in den Bereichen Banken und Versicherungen geeignet.