Path collapse for multidimensional Brownian motion with rebirth

Ilie Grigorescu, Min Kang

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

In a bounded open region of the d-dimensional Euclidean space we consider a Brownian motion which is reborn at a fixed interior point as soon as it reaches the boundary. It was shown that in dimension one coupled paths starting at different points but driven by the same Brownian motion either collapse with probability one or never meet. In higher dimensions, for convex or polyhedral regions, the paths with positive probability of collapse differ at start by a vector from a set of codimension one. The problem can be interpreted in terms of the long term mixing properties of the payoff of a portfolio of knock-out barrier options in derivatives markets.

Original languageEnglish (US)
Pages (from-to)199-209
Number of pages11
JournalStatistics and Probability Letters
Volume70
Issue number3
DOIs
StatePublished - Dec 1 2004

Keywords

  • Absorbing Brownian motion
  • Barrier options
  • Collapsing paths
  • Harmonic measure

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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