Asymptotic properties of integral functionals of geometric stochastic processes

Endre Csáki, Miklós Csörgő, Antónia Földes, Pál Révész

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Abstract

We study strong asymptotic properties of two types of integral functionals of geometric stochastic processes. These integral functionals are of interest in financial modelling, yielding various option pricings, annuities, etc., by appropriate selection of the processes in their respective integrands. We show that under fairly general conditions on the latter processes the logs of the integral functionals themselves asymptotically behave like appropriate sup functionals of the processes in the exponents of their respective integrands. We illustrate the possible use and applications of these strong invariance theorems by listing and elaborating on several examples.

Original languageEnglish
Pages (from-to)480-493
Number of pages14
JournalJournal of Applied Probability
Volume37
Issue number2
DOIs
Publication statusPublished - Jan 1 2000

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Keywords

  • Black-Scholes financial model
  • Geometric Brownian motion
  • Geometric Gaussian and diffusion processes
  • Geometric fractional Brownian motion
  • Geometric processes
  • Integral and sup functionals
  • LIL and strong increments
  • Strong invariance
  • Strong theorems

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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