Research Article

Machine learning for investment models with return of premium clauses under different assumptions

Obonin Samuel Sabastine1, Bright Okore Osu2, Chigozie Chibuisi3*
1 Department of Mathematics and Statistics, Federal University Otuoke, Bayelsa State, Nigeria
2 Abia State University Uturu
3 Federal University of Technology Owerri
* Corresponding author: chigozie.chibuisi@futo.edu.ng
Published: Nov, 2026
DOI: 10.68839/jpstma.2026.jmwd74ha
Pages: 47-58
Views: 29
Downloads: 8

Abstract

In real financial markets, pension funds are simultaneously exposed to stochastic volatility, stochastic interest rates, inflation, wage volatility, mortality hazard, administrative fee leakages, and refund obligations resulting to frequent unfeasible optimal controls that demand infinite leverage or shorting during market downturns. This study develops a continuous-time machine learning framework for optimal dynamic asset allocation in Defined Contribution (DC) pension schemes incorporating return-of-premium clauses under different stochastic market assumptions. The model integrates Heston stochastic volatility, affine stochastic interest rates under the Vasicek and Cox–Ingersoll–Ross frameworks, stochastic wage contributions, De Moivre and Weibull mortality laws, guaranteed interest on refunded contributions, and administrative charges on contributions and accumulated balances. The resulting high-dimensional stochastic optimal control problem is difficult to solve analytically using conventional Hamilton–Jacobi–Bellman (HJB) methods, particularly when portfolio weights must satisfy regulatory restrictions on short-selling and borrowing. To address these challenges, a continuous Deep Reinforcement Learning (DRL) framework based on Proximal Policy Optimization (PPO) and Dirichlet policy distributions is formulated. The model is assessed against established analytical benchmarks and compared with fixed-mix, target-date glidepath, and clipped analytical investment strategies. According to the supplied study, benchmark verification produces mean absolute errors below 0.004, while simulations over 100,000 out-of-sample trajectories report expected terminal wealth of 5.214, terminal wealth variance of 1.118, a terminal Sharpe ratio of 1.632, maximum drawdown of 15.8%, and a sample solvency rate of 100% for the proposed DRL strategy. These reported results indicate that adaptive machine learning may improve portfolio performance and risk management in pension schemes with refund guarantees, stochastic market conditions, and administrative costs. In the generalized stochastic market, empirical Monte Carlo simulations across 100,000 trajectories demonstrate that the DRL agent outperforms traditional fixed-mix and linear glidepath strategies, generating higher terminal wealth, reducing variance, eliminating insolvency risk, and adaptively hedging against volatility spikes and fee-induced wealth drag.

Keywords

Machine learning; defined contribution pension schemes; return-of-premium clauses; stochastic optimal control; deep reinforcement learning; dynamic asset allocation

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How to Cite

Sabastine, O. S., Osu, B. O., & Chibuisi, C. (2026). Machine learning for investment models with return of premium clauses under different assumptions. Journal of Physical Sciences: Theories, Methods and Applications, 1(1), 47-58. https://doi.org/10.68839/jpstma.2026.jmwd74ha

O. S. Sabastine, B. O. Osu, and C. Chibuisi, "Machine learning for investment models with return of premium clauses under different assumptions," Journal of Physical Sciences: Theories, Methods and Applications, vol. 1, no. 1, pp. 47-58, November 2026. doi: 10.68839/jpstma.2026.jmwd74ha

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