Geometric BSDEs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914028061720576 |
|---|---|
| author | Laeven, Roger J. A. Gianin, Emanuela Rosazza Zullino, Marco |
| author_facet | Laeven, Roger J. A. Gianin, Emanuela Rosazza Zullino, Marco |
| contents | We introduce and develop the concepts of Geometric Backward Stochastic Differential Equations (GBSDEs, for short) and two-driver BSDEs. We demonstrate their natural suitability for modeling continuous-time dynamic return risk measures. We characterize a broad spectrum of associated, auxiliary ordinary BSDEs with drivers exhibiting growth rates involving terms of the form $y|\ln(y)|+|z|^2/y$. We establish the existence, regularity, uniqueness, and stability of solutions to this rich class of ordinary BSDEs, considering both bounded and unbounded coefficients and terminal conditions. We exploit these results to obtain corresponding results for the original two-driver BSDEs. Finally, we apply our findings within a GBSDE framework for representing the dynamics of return and star-shaped risk measures including (robust) $L^{p}$-norms, and analyze functional properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09260 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric BSDEs Laeven, Roger J. A. Gianin, Emanuela Rosazza Zullino, Marco Probability Risk Management 60H10, 60H30, 91B06, 91B30, 62P05 We introduce and develop the concepts of Geometric Backward Stochastic Differential Equations (GBSDEs, for short) and two-driver BSDEs. We demonstrate their natural suitability for modeling continuous-time dynamic return risk measures. We characterize a broad spectrum of associated, auxiliary ordinary BSDEs with drivers exhibiting growth rates involving terms of the form $y|\ln(y)|+|z|^2/y$. We establish the existence, regularity, uniqueness, and stability of solutions to this rich class of ordinary BSDEs, considering both bounded and unbounded coefficients and terminal conditions. We exploit these results to obtain corresponding results for the original two-driver BSDEs. Finally, we apply our findings within a GBSDE framework for representing the dynamics of return and star-shaped risk measures including (robust) $L^{p}$-norms, and analyze functional properties. |
| title | Geometric BSDEs |
| topic | Probability Risk Management 60H10, 60H30, 91B06, 91B30, 62P05 |
| url | https://arxiv.org/abs/2405.09260 |