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General Processes: Mathematical Facts

  • Monique JeanblancEmail author
  • Marc Yor
  • Marc Chesney
Chapter
  • 3.7k Downloads
Part of the Springer Finance book series (FINANCE)

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.

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Copyright information

© Springer-Verlag London 2009

Authors and Affiliations

  1. 1.Dépt. MathématiquesUniversité d’EvryEvryFrance
  2. 2.Labo. Probabilités et Modèles AléatoiresUniversité Paris VIParisFrance
  3. 3.Inst. Schweizerisches Bankwesen (ISB)Universität ZürichZürichSwitzerland

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