Optimal Merton's Problem under Multivariate Affine Volterra Models with Jumps

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Highly relevant for quantitative trading in markets exhibiting rough volatility and jump risk. The paper provides semi-closed-form optimal portfolio strategies that account for both path roughness (via fractional kernels) and volatility jumps (via Poisson random measures). The results on how roughness and jumps affect investment demand under different utility functions (power vs. exponential) are directly applicable to portfolio construction. The indifference pricing framework is relevant for derivative hedging. However, the theoretical complexity and lack of empirical validation limit immediate practical implementation.

Extremely high complexity. Requires solving multivariate Riccati-Volterra integral equations with Lévy exponential jump compensators, simulating non-Markovian Volterra processes with jumps using K-integrated Euler-Maruyama schemes, implementing fractional Adams-Bashforth-Moulton methods, and handling BSDEJs with quadratic generators. The mathematical machinery involves convolution calculus, resolvent theory, stochastic Fubini theorems, and Novikov-type criteria for Lévy processes. Practical implementation would require significant expertise in stochastic analysis, numerical methods for fractional equations, and jump-diffusion simulation.

The paper provides detailed mathematical formulations, parameter settings for numerical experiments (Section 4), and describes the numerical schemes (K-integrated Euler-Maruyama for Volterra process, fractional Adams-Bashforth-Moulton for Riccati-Volterra equations). However, no code repository is provided, and the numerical experiments are limited to a two-dimensional case. The theoretical results are fully derivable from the proofs provided.