Drawdowns of diffusions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929607350943744 |
|---|---|
| author | Salminen, Paavo Vallois, Pierre |
| author_facet | Salminen, Paavo Vallois, Pierre |
| contents | In this paper we give excursion theoretical proofs of Lehoczky's formula (in an extended form allowing a lower bound for the underlying diffusion) for the joint distribution of the first drawdown time and the maximum before this time, and of Malyutin's formula for the joint distribution of the first hitting time and the maximum drawdown before this time. It is remarkable -- but there is a clean explanation -- that the excursion theoretical approach which we developed first for Lehoczky's formula provides also a proof for Malyutin's formula. Moreover, we discuss some generalizations and analyze the pure jump process describing the maximum before the first drawdown time when the size of the drawdown is varying |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18374 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Drawdowns of diffusions Salminen, Paavo Vallois, Pierre Probability 60J60, 60J65, 60G40 In this paper we give excursion theoretical proofs of Lehoczky's formula (in an extended form allowing a lower bound for the underlying diffusion) for the joint distribution of the first drawdown time and the maximum before this time, and of Malyutin's formula for the joint distribution of the first hitting time and the maximum drawdown before this time. It is remarkable -- but there is a clean explanation -- that the excursion theoretical approach which we developed first for Lehoczky's formula provides also a proof for Malyutin's formula. Moreover, we discuss some generalizations and analyze the pure jump process describing the maximum before the first drawdown time when the size of the drawdown is varying |
| title | Drawdowns of diffusions |
| topic | Probability 60J60, 60J65, 60G40 |
| url | https://arxiv.org/abs/2411.18374 |