Stochastic Processes for Finance Patrick Roger Download free books at Stochastic Processes for Finance Patrick Roger Strasbourg University, EM Strasbourg Business School June 2010 Download free eBooks at bookboon.com Stochastic Processes for Finance © 2010 Patrick Roger & Ventus Publishing ApS ISBN 978-87-7681-666-7 Download free eBooks at bookboon.com Contents Stochastic Processes for Finance Contents Introduction 1.1 1.2 1.3 1.3.1 1.3.2 1.4 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.5 1.5.1 1.5.2 1.5.3 1.5.4 Discrete-time stochastic processes Introduction The general framework Information revelation over time Filtration on a probability space Adapted and predictable processes Markov chains Introduction Deinition and transition probabilities Chapman-Kolmogorov equations Classiication of states Stationary distribution of a Markov chain Martingales Doob decomposition of an adapted process Martingales and self-inancing strategies Investment strategies and stopping times Stopping times and American options 9 10 12 12 14 17 17 19 19 21 24 25 29 30 34 39 2.1 Continuous-time stochastic processes Introduction 43 43 www.sylvania.com We not reinvent the wheel we reinvent light Fascinating lighting offers an ininite spectrum of possibilities: Innovative technologies and new markets provide both opportunities and challenges An environment in which your expertise is in high demand Enjoy the supportive working atmosphere within our global group and beneit from international career paths Implement sustainable ideas in close cooperation with other specialists and contribute to inluencing our future Come and join us in reinventing light every day Light is OSRAM Click on the ad to read more Download free eBooks at bookboon.com Contents Stochastic Processes for Finance 2.2 2.2.1 2.2.2 2.2.3 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 2.3.6 2.3.7 General framework Filtrations, adapted and predictable processes Markov and diffusion processes Martingales The Brownian motion Intuitive presentation The assumptions Deinition and general properties Usual transformations of the Wiener process The general Wiener process Stopping times Properties of the Brownian motion paths 44 48 51 53 55 55 57 61 64 67 69 71 3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.3 3.3.1 3.3.2 3.3.3 3.4 Stochastic integral and Itô’s lemma Introduction The stochastic integral An intuitive approach Counter-example Deinition and properties of the stochastic integral Calculation rules Itô’s lemma Taylor’s formula, an intuitive approach to Itô’s lemma Itô’s lemma Applications The Girsanov theorem 73 73 75 75 78 80 83 85 86 88 88 91 360° thinking Discover the truth at www.deloitte.ca/careers © Deloitte & Touche LLP and affiliated entities Click on the ad to read more Download free eBooks at bookboon.com .. .Stochastic Processes for Finance Patrick Roger Strasbourg University, EM Strasbourg Business School June 2010 Download free eBooks at bookboon.com Stochastic Processes for Finance ©... bookboon.com Contents Stochastic Processes for Finance Contents Introduction 1.1 1.2 1.3 1.3.1 1.3.2 1.4 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.5 1.5.1 1.5.2 1.5.3 1.5.4 Discrete-time stochastic processes Introduction... Contents Stochastic Processes for Finance 2.2 2.2.1 2.2.2 2.2.3 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 2.3.6 2.3.7 General framework Filtrations, adapted and predictable processes Markov and diffusion processes