Paper: arXiv 2303.08968

Authors: Pieter M. van Staden, Peter A. Forsyth, Yuying Li

Abstract

We present a parsimonious neural network approach, which does not rely on dynamic programming techniques, to solve dynamic portfolio optimization problems subject to multiple investment constraints. The number of parameters of the (potentially deep) neural network remains independent of the number of portfolio rebalancing events, and in contrast to, for example, reinforcement learning, the approach avoids the computation of high-dimensional conditional expectations. As a result, the approach remains practical even when considering large numbers of underlying assets, long investment time horizons or very frequent rebalancing events. We prove convergence of the numerical solution to the theoretical optimal solution of a large class of problems under fairly general conditions, and present ground truth analyses for a number of popular formulations, including mean-variance and mean-conditional value-at-risk problems. We also show that it is feasible to solve Sortino ratio-inspired objectives (penalizing only the variance of wealth outcomes below the mean) in dynamic trading settings with the proposed approach. Using numerical experiments, we demonstrate that if the investment objective functional is separable in the sense of dynamic programming, the correct time-consistent optimal investment strategy is recovered, otherwise we obtain the correct pre-commitment (time-inconsistent) investment strategy. The proposed approach remains agnostic as to the underlying data generating assumptions, and results are illustrated using (i) parametric models for underlying asset returns, (ii) stationary block bootstrap resampling of empirical returns, and (iii) generative adversarial network (GAN)-generated synthetic asset returns.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10 (capped from 7.0: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel, parsimonious neural network architecture that circumvents dynamic programming and reinforcement learning bottlenecks in dynamic portfolio optimization. It backs its framework with rigorous theoretical convergence proofs and empirical validation using parametric models, bootstrap resampling, and GAN-generated synthetic returns.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve high-dimensional dynamic portfolio optimization without Dynamic Programming] --> B[Data Inputs: Parametric returns, Bootstrap resampling & GAN synthetic data]
    B --> C[Methodology: Train Parsimonious Neural Network with fixed parameter size across rebalancing events]
    C --> D[Computational Process: Direct Optimization bypassing high-dimensional conditional expectations]
    D --> E[Outcome 1: Proven convergence to ground-truth optimal solutions]
    D --> F[Outcome 2: Solves separable time-consistent & non-separable pre-commitment problems e.g., CVaR, Sortino]