General Processes: Mathematical Facts

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 9 in Mathematical Methods for Financial Markets, 2009, pp 509-550 from Springer

Abstract: Abstract In this chapter, we consider studies involving càdlàg processes. We pay particular attention to semi-martingales with respect to a given filtration; these processes will always be taken with càdlàg paths. We present the definition of stochastic integrals with respect to a square integrable martingale, and we extend the definition to stochastic integrals with respect to a local martingale. Then, we introduce semi-martingales, quadratic covariation processes for semi-martingales and some general versions of Itô’s formula and Girsanov’s theorem. We give necessary and sufficient conditions for the existence of an equivalent martingale measure. We end the chapter with a brief survey of valuation in an incomplete market.

Date: 2009
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DOI: 10.1007/978-1-84628-737-4_9

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