On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917467447623680 |
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| author | Gnabeyeu, Emmanuel |
| author_facet | Gnabeyeu, Emmanuel |
| contents | This paper is concerned with Merton's portfolio optimization problem in a Volterra stochastic environment described by a multivariate fake stationary Volterra--Heston model. Due to the non-Markovianity and non-semimartingality of the underlying processes, the classical stochastic control approach cannot be directly applied in this setting. Instead, the problem is tackled using a stochastic factor solution to a Riccati backward stochastic differential equation (BSDE). Our approach is inspired by the martingale optimality principle combined with a suitable verification argument. The resulting optimal strategies for Merton's problems are derived in semi-closed form depending on the solutions to time-dependent multivariate Riccati-Volterra equations, while the optimal value is expressed using the solution to this original Riccati BSDE. Numerical results on a two dimensional fake stationary rough Heston model illustrate the impact of stationary rough volatilities on the optimal Merton strategies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_11046 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models Gnabeyeu, Emmanuel Optimization and Control Probability Computational Finance 34A08, 34A34, 45D05, 60G10, 60G22, 60H10, 91B70, 91G80, 93E20 This paper is concerned with Merton's portfolio optimization problem in a Volterra stochastic environment described by a multivariate fake stationary Volterra--Heston model. Due to the non-Markovianity and non-semimartingality of the underlying processes, the classical stochastic control approach cannot be directly applied in this setting. Instead, the problem is tackled using a stochastic factor solution to a Riccati backward stochastic differential equation (BSDE). Our approach is inspired by the martingale optimality principle combined with a suitable verification argument. The resulting optimal strategies for Merton's problems are derived in semi-closed form depending on the solutions to time-dependent multivariate Riccati-Volterra equations, while the optimal value is expressed using the solution to this original Riccati BSDE. Numerical results on a two dimensional fake stationary rough Heston model illustrate the impact of stationary rough volatilities on the optimal Merton strategies. |
| title | On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models |
| topic | Optimization and Control Probability Computational Finance 34A08, 34A34, 45D05, 60G10, 60G22, 60H10, 91B70, 91G80, 93E20 |
| url | https://arxiv.org/abs/2603.11046 |