Multi-Period Portfolio Optimization Model with Cone Constraints and Discrete Decisions

Ümit Sağlam () and Hande Y. Benson
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Ümit Sağlam: Department of Management and Supply Chain, College of Business and Technology, East Tennessee State University, Johnson City, TN 37614, USA
Hande Y. Benson: Department of Decision Sciences and MIS, LeBow College of Business, Drexel University, Philadelphia, PA 19104, USA

JRFM, 2025, vol. 18, issue 4, 1-16

Abstract: This work develops a practical multi-period optimization approach that incorporates real-world constraints, including discrete decisions and conic risk constraints. Expanding upon earlier single-period models, our framework employs a binary scenario tree derived from monthly returns of randomly selected S&P 500 stocks to represent market evolution across multiple periods. The formulation captures essential portfolio constraints, such as transaction fees, sector diversification, and minimum investment thresholds, resulting in a robust and comprehensive optimization approach. To efficiently solve the resulting mixed-integer second-order cone programming (MISOCP) problem, we employ an outer approximation algorithm with a warmstart strategy, which significantly improves solution runtimes and computational efficiency. Numerical experiments demonstrate the model’s effectiveness, showing an average improvement of 10.71 % in iteration count and 15.24 % in computational time when using the warmstart approach.

Keywords: mixed-integer linear and nonlinear optimizer (MILANO); mixed-integer second-order cone programming (MISOCP); multi-period portfolio optimization (MPO); outer approximation (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2025
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