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Complements on Brownian Motion

Author

Listed:
  • Monique Jeanblanc

    (Université d’Evry)

  • Marc Yor

    (Université Paris VI)

  • Marc Chesney

    (Universität Zürich)

Abstract

In the first part of this chapter, we present the definition of local time and the associated Tanaka formulae, first for Brownian motion, then for more general continuous semi-martingales. In the second part, we give definitions and basic properties of Brownian bridges and Brownian meander. This is motivated by the fact that, in order to study complex derivative instruments, such as passport options or Parisian options, some knowledge of local times, bridges and excursions with respect to BM in particular and more generally for diffusions, is useful. We give some applications to exotic options, in particular to Parisian options.

Suggested Citation

Handle: RePEc:spr:sprfcp:978-1-84628-737-4_4
DOI: 10.1007/978-1-84628-737-4_4
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