On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients
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_ | 1866910537492725760 |
|---|---|
| author | Alfonsi, Aurélien Szulda, Guillaume |
| author_facet | Alfonsi, Aurélien Szulda, Guillaume |
| contents | We consider one-dimensional stochastic Volterra equations with jumps for which we establish conditions upon the convolution kernel and coefficients for the strong existence and pathwise uniqueness of a non-negative càdlàg solution. By using the approach recently developed in arXiv:2302.07758, we show the strong existence by using a nonnegative approximation of the equation whose convergence is proved via a variant of the Yamada--Watanabe approximation technique. We apply our results to Lévy-driven stochastic Volterra equations. In particular, we are able to define a Volterra extension of the so-called alpha-stable Cox--Ingersoll--Ross process, which is especially used for applications in Mathematical Finance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19203 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients Alfonsi, Aurélien Szulda, Guillaume Probability Mathematical Finance We consider one-dimensional stochastic Volterra equations with jumps for which we establish conditions upon the convolution kernel and coefficients for the strong existence and pathwise uniqueness of a non-negative càdlàg solution. By using the approach recently developed in arXiv:2302.07758, we show the strong existence by using a nonnegative approximation of the equation whose convergence is proved via a variant of the Yamada--Watanabe approximation technique. We apply our results to Lévy-driven stochastic Volterra equations. In particular, we are able to define a Volterra extension of the so-called alpha-stable Cox--Ingersoll--Ross process, which is especially used for applications in Mathematical Finance. |
| title | On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients |
| topic | Probability Mathematical Finance |
| url | https://arxiv.org/abs/2402.19203 |