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arXiv · 2603.11046

On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models

Emmanuel Gnabeyeu
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Abstract

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.

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Emmanuel Gnabeyeu. 2026-03-11. On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models. https://arxiv.org/abs/2603.11046

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