On the maximum increase and decrease of one-dimensional diffusions

Paavo Salminen, Pierre Vallois

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this paper the joint distribution of the maximum increase and the maximum decrease up to a first hitting time is calculated for a regular one-dimensional diffusion. Moreover, it is shown that the process given by the maximum decrease when the hitting level is the "time" parameter is a pure jump Markov process and its generator is found. As examples, Brownian motion and three dimensional Bessel process are analyzed more in detail.
Translated title of the contributionOn maximum increase and decrease of one-dimensional diffusions
Original languageEnglish
Pages (from-to)5592-5604
Number of pages13
JournalStochastic Processes and their Applications
Volume130
Issue number9
DOIs
Publication statusPublished - 9 Sep 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • maximum drawup
  • maximum drawdown
  • optional sampling

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