On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models

Battle Count: 70

The paper is highly relevant to quantitative trading in terms of portfolio optimization under realistic (rough) volatility dynamics. It provides explicit optimal strategies for multi-asset portfolios with leverage effects and heterogeneous roughness across assets. However, the theoretical nature, reliance on specific model assumptions (affine structure, linear risk premium), and lack of empirical validation limit direct practical implementation. The results are most relevant for institutional portfolio managers and quantitative researchers working on long-horizon asset allocation under rough volatility. The fake stationary framework is particularly relevant for long-term investment analysis where classical rough volatility models lack stationarity.

Extremely high implementation complexity. Requires: (1) Simulation of non-Markovian, non-semimartingale Volterra processes via Wiener-Hopf transform and semi-integrated Euler schemes; (2) Numerical solution of multivariate Riccati-Volterra equations using fractional Adams-Bashforth-Moulton methods; (3) Solving functional integral equations for the stabilizer function; (4) Handling the Riccati BSDE with quadratic generator; (5) Computing adjusted forward processes; (6) Implementing Girsanov transformations for measure changes. The mathematical prerequisites include advanced stochastic analysis, Volterra integral equations, fractional calculus, and BSDE theory.

The paper is primarily theoretical with rigorous mathematical proofs. Numerical experiments in Section 4 use a two-dimensional fake stationary rough Heston model with specified parameters (c, mu_0, D, Sigma, theta, nu) and fractional kernels. The simulation uses a Wiener-Hopf transform-based Euler-Maruyama scheme and the fractional Adams-Bashforth-Moulton method for the Riccati-Volterra system. However, no code or repository is provided, and the numerical implementation details (e.g., Cholesky decomposition for Gaussian integrals) reference other papers. Reproducing the full theoretical framework requires advanced knowledge of Volterra equations, BSDEs, and fractional calculus.