Self-Consistent Adjoint Policy Iteration for Constrained Dynamic Portfolio Choice

Battle Count: 77

Directly addresses continuous-time dynamic portfolio choice with realistic constraints (short-sale, borrowing, position limits) and predictable returns. The method provides a principled simulation-based approach that avoids full factor-grid HJB discretization while maintaining convergence guarantees. The three-factor, fifty-asset benchmark demonstrates scalability. The distinction between current-policy re-evaluation and pooled refinement is practically relevant for implementation. The CRRA reduction to a low-dimensional hedging field plus explicit QP is directly applicable to institutional portfolio management.

High complexity due to multiple interacting components: (1) fixed-latent OL-BPTT through discretized rollouts, (2) conditional adjoint field estimation via regression/interpolation, (3) constrained QP solving via metric projection, (4) damped policy updates, (5) coupled Richardson time-grid correction, (6) tilted Feynman-Kac sampling, (7) output policy construction via pre-projection field averaging and interpolation. The theoretical framework requires understanding of BSDEs, PMP adjoints, HJB equations, and parabolic PDE regularity. However, the CRRA reduction simplifies the core computation to a low-dimensional field estimate plus a standard QP.

Code is publicly available on GitHub. The paper provides detailed algorithm pseudocode (Algorithm 1), theorem-matched numerical audits with specific seeds (260730, 260731, 260732), and comprehensive supplementary diagnostics. However, the theoretical framework is highly specialized (CRRA, affine factors, convex constraints) and the numerical implementation involves multiple interacting components (OL-BPTT, QP solvers, Richardson correction, tilted sampling) that require careful configuration.