MATHEMATICS FOR FINANCE: A REVIEW OF QUANTITATIVE METHODS IN LOAN PORTFOLIO OPTIMIZATION

Abstract

This systematic literature review investigates the evolution and application of quantitative methods in loan portfolio optimization, covering studies published between 2000 and 2024. The research adheres to PRISMA 2020 guidelines and integrates 87 peer-reviewed articles selected through rigorous eligibility and quality criteria. The objective is to synthesize key methodological advances, sectoral applications, and regulatory impacts that shape optimization strategies in credit risk management. The findings reveal that stochastic optimization remains the most dominant methodological approach, cited in 42 studies with over 5,300 cumulative citations. These models offer superior capabilities in modeling credit transitions and macroeconomic volatility, particularly through two-stage and multi-stage programming. Their robustness in simulating stress scenarios has made them indispensable for risk-sensitive portfolio construction. Simultaneously, the adoption of machine learning techniques has grown rapidly, especially post-2015, driven by the rise of fintech and data availability. With 28 studies contributing over 4,800 citations, algorithms such as decision trees, support vector machines, and neural networks have demonstrated superior accuracy in credit scoring and borrower segmentation. These models enable high-dimensional pattern recognition and outperform traditional regression methods in predictive tasks. A key insight from the review is the pervasive integration of regulatory frameworks, particularly Basel II and Basel III. Thirty-five studies embed elements like risk-weighted assets (RWA), capital adequacy ratios, and stress testing protocols directly into optimization objectives. This alignment between model structure and supervisory requirements ensures compliance and robustness under regulatory scrutiny. The review also highlights significant sectoral customization in optimization models. Commercial banks prioritize capital efficiency and exposure management, while microfinance institutions focus on simplicity and inclusivity. underscores the coexistence of traditional risk models with advanced AI-driven approaches, the operationalization of regulatory norms within optimization strategies, and the transformative role of real-time analytics in reshaping credit decision-making. As financial institutions face mounting uncertainty, this synthesis offers actionable insights for aligning quantitative rigor with evolving market and regulatory demands.