Convergence of Neural Network Policies for Risk–Reward Optimization

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The paper is primarily focused on retirement decumulation and risk-reward optimization rather than high-frequency trading or alpha generation. However, the convergence framework for NN-parametrized constrained feedback policies is broadly applicable to portfolio optimization, risk management, and any discrete-intervention stochastic control problem in finance. The CVaR-based risk-reward objective and constrained two-step policy structure are relevant to institutional portfolio management. The theoretical convergence guarantees provide a foundation for NN-based policy approximation in quantitative finance settings.

Implementation requires: (1) designing two coupled FNNs with custom output layers (sigmoid for interval constraints, softmax for simplex constraints); (2) implementing the controlled state recursion with piecewise-defined dynamics; (3) constructing the finite-dimensional performance vector and scalarized risk-reward objective; (4) joint optimization over NN parameters and auxiliary variable ξ using Adam; (5) Monte Carlo scenario generation from a Kou jump-diffusion model; (6) for validation, implementing a grid-based backward recursion reference solver. The mathematical framework is sophisticated with multiple layers of convergence analysis, though the actual NN training is standard.

The paper provides detailed hyperparameters (Table 5.3), calibration parameters (Table 5.1), retirement scenario specifications (Table 5.2), and full mathematical formulations. However, no code repository is mentioned, and the grid-based reference method implementation details are partially described. The Kou jump-diffusion calibration uses Australian market data from Bloomberg and ABS, which may not be freely accessible. The convergence proofs are fully detailed in appendices.