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Integrated Prediction and Multi-period Portfolio Optimization

12 December 2025
Yuxuan Linghu
Zhiyuan Liu
Qi Deng
    AI4TS
ArXiv (abs)PDFHTML
Main:20 Pages
7 Figures
Bibliography:3 Pages
4 Tables
Abstract

Multi-period portfolio optimization is important for real portfolio management, as it accounts for transaction costs, path-dependent risks, and the intertemporal structure of trading decisions that single-period models cannot capture. Classical methods usually follow a two-stage framework: machine learning algorithms are employed to produce forecasts that closely fit the realized returns, and the predicted values are then used in a downstream portfolio optimization problem to determine the asset weights. This separation leads to a fundamental misalignment between predictions and decision outcomes, while also ignoring the impact of transaction costs. To bridge this gap, recent studies have proposed the idea of end-to-end learning, integrating the two stages into a single pipeline. This paper introduces IPMO (Integrated Prediction and Multi-period Portfolio Optimization), a model for multi-period mean-variance portfolio optimization with turnover penalties. The predictor generates multi-period return forecasts that parameterize a differentiable convex optimization layer, which in turn drives learning via portfolio performance. For scalability, we introduce a mirror-descent fixed-point (MDFP) differentiation scheme that avoids factorizing the Karush-Kuhn-Tucker (KKT) systems, which thus yields stable implicit gradients and nearly scale-insensitive runtime as the decision horizon grows. In experiments with real market data and two representative time-series prediction models, the IPMO method consistently outperforms the two-stage benchmarks in risk-adjusted performance net of transaction costs and achieves more coherent allocation paths. Our results show that integrating machine learning prediction with optimization in the multi-period setting improves financial outcomes and remains computationally tractable.

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