On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models
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.引用本文复制引用
Emmanuel Gnabeyeu.On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models[EB/OL].(2026-03-11)[2026-03-13].https://arxiv.org/abs/2603.11046.学科分类
数学
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