Stochastic Processes for Finance
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788776816667
Table of contents: title: Content; title: Introduction; title: 1 Discrete-time stochastic processes; title: 1.1 Introduction; title: 1.2 The general framework; title: 1.3 Information revelation over time; title: 1.3.1 Filtration on a probability space; title: 1.3.2 Adapted and predictable processes; title: 1.4 Markov chains; title: 1.4.1 Introduction; title: 1.4.2 Definition and transition probabilities; title: 1.4.3 Chapman-Kolmogorov equations; title: 1.4.4 Classification of states; title: 1.4.5 Stationary distribution of a Markov chain; title: 1.5 Martingales; title: 1.5.1 Doob decomposition of an adapted process; title: 1.5.2 Martingales and self-financing strategies; title: 1.5.3 Investment strategies and stopping times; title: 1.5.4 Stopping times and American options; title: 2 Continuous-time stochastic processes; title: 2.1 Introduction; title: 2.2 General framework; title: 2.2.1 Filtrations, adapted and predictable processes; title: 2.2.2 Markov and diffusion processes; title: 2.2.3 Martingales; title: 2.3 The Brownian motion; title: 2.3.1 Intuitive presentation; title: 2.3.2 The assumptions; title: 2.3.3 Definition and general properties; title: 2.3.4 Usual transformations of the Wiener process; title: 2.3.5 The general Wiener process; title: 2.3.6 Stopping times; title: 2.3.7 Properties of the Brownian motion paths; title: 3 Stochastic integral and Itô’s lemma; title: 3.1 Introduction; title: 3.2 The stochastic integral; title: 3.2.1 An intuitive approach; title: 3.2.2 Counter-example; title: 3.2.3 Definition and properties of the stochastic integral; title: 3.2.4 Calculation rules; title: 3.3 Itô’s lemma; title: 3.3.1 Taylor’s formula, an intuitive approach to Itô’s lemma; title: 3.3.2 Itô’s lemma; title: 3.3.3 Applications; title: 3.4 The Girsanov theorem; title: 3.4.1 Preliminaries; title: 3.4.2 Girsanov theorem; title: 3.4.3 Application; title: 3.5 Stochastic differential equations; title: 3.5.1 Existence and unicity of solutions; title: 3.5.2 A specific case: linear equations; title: Bibliography; title: Index