Optimal Merton's Problem under Multivariate Affine Volterra Models with Jumps
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| Format: | Preprint |
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2026
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| author | Dro, Sigui Brice Gnabeyeu, Emmanuel |
| author_facet | Dro, Sigui Brice Gnabeyeu, Emmanuel |
| contents | This paper is concerned with portfolio selection for an investor with exponential, power, and logarithmic utility in multi-asset financial markets allowing jumps. We investigate the classical Merton's portfolio optimization problem in a Volterra stochastic environment described by a multivariate Volterra--Heston model with jumps driven by an independent Poisson random measure. Owing to the non-Markovian and non-semimartingale nature of the model, classical stochastic control techniques are not directly applicable. Instead, the problem is tackled using the martingale optimality principle by constructing a family of supermartingale processes characterized via solutions to an original Riccati backward stochastic differential equation with jumps (Riccati BSDEJ).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 BSDEJ. Numerical experiments on a two-dimensional rough Heston model illustrate the impact of both path roughness and jumps components on the value function and optimal strategies in the Merton problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_00688 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Merton's Problem under Multivariate Affine Volterra Models with Jumps Dro, Sigui Brice Gnabeyeu, Emmanuel Optimization and Control Probability Mathematical Finance 34A08, 34A34, 45D05, 60G10, 60G22, 60H10, 91B70, 91G80, 93E20 This paper is concerned with portfolio selection for an investor with exponential, power, and logarithmic utility in multi-asset financial markets allowing jumps. We investigate the classical Merton's portfolio optimization problem in a Volterra stochastic environment described by a multivariate Volterra--Heston model with jumps driven by an independent Poisson random measure. Owing to the non-Markovian and non-semimartingale nature of the model, classical stochastic control techniques are not directly applicable. Instead, the problem is tackled using the martingale optimality principle by constructing a family of supermartingale processes characterized via solutions to an original Riccati backward stochastic differential equation with jumps (Riccati BSDEJ).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 BSDEJ. Numerical experiments on a two-dimensional rough Heston model illustrate the impact of both path roughness and jumps components on the value function and optimal strategies in the Merton problem. |
| title | Optimal Merton's Problem under Multivariate Affine Volterra Models with Jumps |
| topic | Optimization and Control Probability Mathematical Finance 34A08, 34A34, 45D05, 60G10, 60G22, 60H10, 91B70, 91G80, 93E20 |
| url | https://arxiv.org/abs/2605.00688 |