Adaptive Multilevel Stochastic Approximation of the Value-at-Risk
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_ | 1866915932520054784 |
|---|---|
| author | Crépey, Stéphane Frikha, Noufel Louzi, Azar Spence, Jonathan |
| author_facet | Crépey, Stéphane Frikha, Noufel Louzi, Azar Spence, Jonathan |
| contents | Crépey, Frikha, and Louzi (2025) introduced a multilevel stochastic approximation scheme to compute the value-at-risk of a financial loss that is only simulatable by Monte Carlo. The best complexity of the scheme is in O($\varepsilon^{-\frac52}$), $\varepsilon>0$ being a prescribed accuracy, which is suboptimal compared to the canonical multilevel Monte Carlo performance. This suboptimality stems from the discontinuity ofthe Heaviside function involved in the biased stochastic gradient that is recursively evaluated to derive the value-at-risk. To mitigate this issue, this paper proposes and analyzes a multilevel stochastic approximation algorithm that adaptively selects the number of inner samples at each level, and proves that its best complexity is in O($\varepsilon^{-2}|\ln{\varepsilon}|^\frac52$). Our theoretical analysis is exemplified through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06531 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive Multilevel Stochastic Approximation of the Value-at-Risk Crépey, Stéphane Frikha, Noufel Louzi, Azar Spence, Jonathan Risk Management Probability Computational Finance 65C05, 62L20, 62G32, 91G60 Crépey, Frikha, and Louzi (2025) introduced a multilevel stochastic approximation scheme to compute the value-at-risk of a financial loss that is only simulatable by Monte Carlo. The best complexity of the scheme is in O($\varepsilon^{-\frac52}$), $\varepsilon>0$ being a prescribed accuracy, which is suboptimal compared to the canonical multilevel Monte Carlo performance. This suboptimality stems from the discontinuity ofthe Heaviside function involved in the biased stochastic gradient that is recursively evaluated to derive the value-at-risk. To mitigate this issue, this paper proposes and analyzes a multilevel stochastic approximation algorithm that adaptively selects the number of inner samples at each level, and proves that its best complexity is in O($\varepsilon^{-2}|\ln{\varepsilon}|^\frac52$). Our theoretical analysis is exemplified through numerical experiments. |
| title | Adaptive Multilevel Stochastic Approximation of the Value-at-Risk |
| topic | Risk Management Probability Computational Finance 65C05, 62L20, 62G32, 91G60 |
| url | https://arxiv.org/abs/2408.06531 |