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Martingales

  • Sidney I. Resnick
Chapter

Abstract

Martingales are a class of stochastic processes which has had profound influence on the development of probability and stochastic processes. There are few areas of the subject untouched by martingales. We will survey the theory and applications of discrete time martingales and end with some recent developments in mathematical finance. Here is what to expect in this chapter:
  • Absolute continuity and the Radon-Nikodym Theorem.

  • Conditional expectation.

  • Martingale definitions and elementary properties and examples.

  • Martingale stopping theorems and applications.

  • Martingale convergence theorems and applications.

  • The fundamental theorems of mathematical finance.

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Copyright information

© Springer Science+Business Media New York 2005

Authors and Affiliations

  • Sidney I. Resnick
    • 1
  1. 1.School of Operations Research and Industrial EngineeringIthacaUSA

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