Utility Maximization in Multivariate Volterra Models

This paper is concerned with portfolio selection for an investor power utility in multiasset financial markets a rough stochastic environment. We investigate Merton’s problem different multivariate Volterra models, covering the Heston model. First we consider class of affine models introduced [E. Abi Jaber, E. Miller, and H. Pham, SIAM J. Financial Math.., 12 (2021), pp. 369–409]. Based on classical Wishart model described [N. Bäuerle Z. Li, Appl. Probab., 50 (2013), 1025–1043], then introduce new matrix-valued volatility model, where driven by Volterra–Wishart process. Due to non-Markovianity underlying processes, control approach cannot be applied these settings. To overcome this issue, provide verification argument using calculus convolutions resolvents. The resulting optimal strategy can expressed explicitly terms solution Riccati–Volterra equation. thus extend results obtained Han Wong case, avoiding restrictions correlation structure linked martingale distortion transformation used [B. Y. Wong, Finance Res. Lett., 39 (2021)]. also existence uniqueness theorems occurring processes illustrate our numerical study.