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Optimal Merton's Problem under Multivariate Affine Volterra Models with Jumps

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  • Sigui Brice Dro
  • Emmanuel Gnabeyeu

Abstract

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.

Suggested Citation

  • Sigui Brice Dro & Emmanuel Gnabeyeu, 2026. "Optimal Merton's Problem under Multivariate Affine Volterra Models with Jumps," Papers 2605.00688, arXiv.org.
    • Handle: RePEc:arx:papers:2605.00688
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    References listed on IDEAS

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    1. Emmanuel Gnabeyeu & Gilles Pag`es & Mathieu Rosenbaum, 2025. "On Inhomogeneous Affine Volterra Processes: Stationarity and Applications to the Volterra Heston Model," Papers 2512.09590, arXiv.org.
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    8. Emmanuel Gnabeyeu, 2026. "On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models," Papers 2603.11046, arXiv.org, revised May 2026.
    9. Emmanuel Gnabeyeu, 2026. "On the mean-variance problem through the lens of multivariate fake stationary affine Volterra dynamics," Papers 2604.01300, arXiv.org.
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