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On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models

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  • Emmanuel Gnabeyeu

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. Numerical results on a two dimensional fake stationary rough Heston model illustrate the impact of stationary rough volatilities on the optimal Merton strategies.

Suggested Citation

  • Emmanuel Gnabeyeu, 2026. "On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models," Papers 2603.11046, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2603.11046
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    References listed on IDEAS

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