A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications

Battle Count: 109

Highly relevant to quantitative trading and portfolio management. The paper directly addresses utility maximization problems under rough volatility (a realistic market model), provides optimal investment strategies (pi*_t), optimal wealth processes, and consumption rates. The rough Bergomi model used is widely adopted in practice for volatility modeling. The method enables solving complex coupled FBSDEs that arise in optimal portfolio allocation with stochastic volatility, which is directly applicable to algorithmic trading strategy development and risk management.

High implementation complexity due to: (1) simulation of fractional Brownian motion (Riemann-Liouville type with Hurst index H<1/2), (2) coupled forward-backward Euler discretization requiring iterative solutions, (3) neural network training at each time step with increasing input dimensionality, (4) handling of non-Markovian path information {W_s, V_s: 0<=s<=t}, (5) careful parameter tuning for the three coupling conditions, (6) batch normalization and gradient clipping for stability. The theoretical framework requires understanding of BSPDEs, decoupling fields, and stochastic analysis.

The paper provides detailed algorithm descriptions, parameter settings (T=1, rho=-0.9, r=0.05, lambda=8, mu=0.1, sigma=0.2, H=0.07, eta=1.9, xi_t=0.09), network architecture (3 hidden layers, ReLU, batch normalization), training details (Adam optimizer, 64000 samples, 20 epochs, batch size 64), and explicit FBSDE formulations. However, no code repository is provided, and the non-Markovian framework with fractional Brownian motion simulation details could be challenging to reproduce exactly.