Paper
On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models
Authors
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.11046v1</id>\n <title>On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models</title>\n <updated>2026-03-11T17:59:43Z</updated>\n <link href='https://arxiv.org/abs/2603.11046v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.11046v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.OC'/>\n <category scheme='http://arxiv.org/schemas/atom' term='math.PR'/>\n <category scheme='http://arxiv.org/schemas/atom' term='q-fin.CP'/>\n <published>2026-03-11T17:59:43Z</published>\n <arxiv:comment>42 pages, 6 figures</arxiv:comment>\n <arxiv:primary_category term='math.OC'/>\n <author>\n <name>Emmanuel Gnabeyeu</name>\n </author>\n </entry>"
}