On explicit solutions to a class of quadratic BSDEJs driven by affine Volterra processes with jumps and applications

Battle Count: 91

Highly relevant for quantitative trading in several ways: (1) Provides explicit analytical solutions for optimal portfolio allocation in rough volatility models with jumps, which are increasingly realistic market models; (2) The Markowitz mean-variance framework with efficient frontier is directly applicable to portfolio construction; (3) The rough Heston model captures empirically observed volatility roughness; (4) The jump component accounts for market discontinuities; (5) The feedback control form (4.87) is implementable in practice. However, the paper is primarily theoretical and the numerical validation is limited to 2D without jumps.

Very high implementation complexity due to: (1) Non-Markovian, non-semimartingale framework requiring Volterra integral equation solvers; (2) Fractional kernels requiring specialized numerical methods (fractional Adams-Bashforth-Moulton); (3) Multivariate Riccati-Volterra systems with Lévy jump compensators; (4) Simulation of rough volatility paths using K-integrated Euler-Maruyama schemes; (5) The mathematical machinery (BSDEJs, distortion transformations, Girsanov theorem) requires deep expertise in stochastic analysis; (6) Computing the adjusted forward process and exponential-affine transforms adds further complexity.

The paper mentions code is available in a Python notebook (footnote 1), but no explicit GitHub URL is provided. The mathematical framework is fully self-contained with complete proofs. Numerical experiments use a 2D fake stationary rough Heston model with specified parameters. The fractional Adams-Bashforth-Moulton method and K-integrated Euler-Maruyama scheme are described. However, the paper is highly theoretical with complex mathematical derivations that would require significant expertise to reproduce.