Continuous-Path Random Processes: Mathematical Prerequisites

Monique Jeanblanc (), Marc Yor and Marc Chesney
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Monique Jeanblanc: Université d’Evry
Marc Yor: Université Paris VI
Marc Chesney: Universität Zürich

Chapter 1 in Mathematical Methods for Financial Markets, 2009, pp 3-78 from Springer

Abstract: Abstract Historically, in mathematical finance, continuous-time processes have been considered from the very beginning, e.g., Bachelier [39, 41] deals with Brownian motion, which has continuous paths. This may justify making our starting point in this book to deal with continuous-path random processes, for which, in this first chapter, we recall some well-known facts. We try to give all the definitions and to quote all the important facts for further use. In particular, we state, without proofs, results on stochastic calculus, change of probability and stochastic differential equations.

Keywords: Brownian Motion; Local Martingale; Mathematical Prerequisite; Integrable Martingale; Bounded Borel Function (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/978-1-84628-737-4_1

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