On the mean-variance problem through the lens of multivariate fake stationary affine Volterra dynamics

Emmanuel Gnabeyeu ()
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Emmanuel Gnabeyeu: SU - Sorbonne Université

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Abstract: We investigate the continuous-time Markowitz mean-variance portfolio selection problem within a multivariate class of fake stationary affine Volterra models. In this non-Markovian and nonsemimartingale market framework with unbounded random coefficients, the classical stochastic control approach cannot be directly applied to the associated optimization task. Instead, the problem is tackled using a stochastic factor solution to a Riccati backward stochastic differential equation (BSDE). The optimal feedback control is characterized by means of this equation, whose explicit solutions is derived in terms of time-dependent multi-dimensional Riccati-Volterra equations. Specifically, we obtain analytical closed-form expressions for the optimal portfolio policies as well as the mean-variance efficient frontier, both of which depend on the solution to the associated multivariate Riccati-Volterra system. To illustrate our results, numerical experiments based on a two dimensional fake stationary rough Heston model highlight the impact of stabilized rough volatilities and stochastic correlations on the optimal Markowitz strategies.

Keywords: Affine Volterra Processes; Stochastic Control; Stochastic Operations Research; Backward Stochastic Differential Equations (BSDE); Riccati Equations; Functional Integral Equation; Fractional Differential Equations (search for similar items in EconPapers)
Date: 2026-04-09
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