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 contribution | On maximum increase and decrease of one-dimensional diffusions |
|---|---|
| Original language | English |
| Pages (from-to) | 5592-5604 |
| Number of pages | 13 |
| Journal | Stochastic Processes and their Applications |
| Volume | 130 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 9 Sept 2020 |
| MoE publication type | A1 Journal article-refereed |
Keywords
- maximum drawup
- maximum drawdown
- optional sampling