Stochastic Dominance Constrained Optimization with S-shaped Utilities: Poor-Performance-Region Algorithm and Neural Network

Battle Count: 60

Highly relevant to quantitative trading and portfolio management. The paper directly addresses portfolio selection under realistic behavioral preferences (S-shaped utility from prospect theory) with implementable risk constraints (FSD/SSD). The FSD solution provides a practical alternative to liquidation boundaries for risk management. The PPRA algorithm offers a computationally tractable approach to SSD-constrained optimization. The neural network framework enables scalable solution of complex portfolio problems. The financial insight of following benchmark in poor states and classical policy otherwise is directly actionable for trading strategies. However, the static complete-market setting limits direct applicability to dynamic trading.

High implementation complexity due to: (1) PPRA requires careful partitioning of the poor performance region, computation of tangent points, iterative correction of the correction function, and monotonicity verification; (2) The piecewise neural network framework requires implementing multiple sub-networks with Fourier feature embeddings, analytic prior injection, and constraint-aware loss functions; (3) The FSD analytical solution involves state-dependent tangent point computation; (4) Numerical integration for quantile functions and budget constraints; (5) Bisection method for Lagrange multiplier determination. The mathematical sophistication is high, requiring expertise in stochastic optimization, quantile methods, and deep learning.

The paper provides detailed algorithmic descriptions (Algorithm 1 and Algorithm 2), explicit parameter settings for all numerical experiments, and complete mathematical formulations. However, no code repository is provided. The Black-Scholes model setup and parameter values are fully specified, enabling reproduction of numerical results. The neural network architecture details (8 hidden layers, 256 neurons, Tanh, Fourier features) are provided. Reproduction would require implementing PPRA and the piecewise NN framework from scratch.