On the mean-variance problem through the lens of multivariate fake stationary affine Volterra dynamics
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914437655429120 |
|---|---|
| author | Gnabeyeu, Emmanuel |
| author_facet | Gnabeyeu, Emmanuel |
| contents | We investigate the continuous-time Markowitz mean-variance portfolio selection problem within a multivariate class of fake stationary affine Volterra models. In this non-Markovian and non-semimartingale market framework with unbounded random coefficients, the classical stochastic control approach cannot be directly applied to the associated optimization task. Instead, the problem is tackled using a stochastic factor solution to a Riccati backward stochastic differential equation (BSDE). The optimal feedback control is characterized by means of this equation, whose explicit solutions is derived in terms of multi-dimensional Riccati-Volterra equations. Specifically, we obtain analytical closed-form expressions for the optimal portfolio policies as well as the mean-variance efficient frontier, both of which depend on the solution to the associated multivariate Riccati-Volterra system. To illustrate our results, numerical experiments based on a two dimensional fake stationary rough Heston model highlight the impact of rough volatilities and stochastic correlations on the optimal Markowitz strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01300 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the mean-variance problem through the lens of multivariate fake stationary affine Volterra dynamics Gnabeyeu, Emmanuel Optimization and Control Probability Mathematical Finance 34A08, 34A34, 45D05, 60G10, 60G22, 60H10, 91B70, 91G80, 93E20 We investigate the continuous-time Markowitz mean-variance portfolio selection problem within a multivariate class of fake stationary affine Volterra models. In this non-Markovian and non-semimartingale market framework with unbounded random coefficients, the classical stochastic control approach cannot be directly applied to the associated optimization task. Instead, the problem is tackled using a stochastic factor solution to a Riccati backward stochastic differential equation (BSDE). The optimal feedback control is characterized by means of this equation, whose explicit solutions is derived in terms of multi-dimensional Riccati-Volterra equations. Specifically, we obtain analytical closed-form expressions for the optimal portfolio policies as well as the mean-variance efficient frontier, both of which depend on the solution to the associated multivariate Riccati-Volterra system. To illustrate our results, numerical experiments based on a two dimensional fake stationary rough Heston model highlight the impact of rough volatilities and stochastic correlations on the optimal Markowitz strategies. |
| title | On the mean-variance problem through the lens of multivariate fake stationary affine Volterra dynamics |
| topic | Optimization and Control Probability Mathematical Finance 34A08, 34A34, 45D05, 60G10, 60G22, 60H10, 91B70, 91G80, 93E20 |
| url | https://arxiv.org/abs/2604.01300 |