Inclusion-Exclusion Principle for Sharia Portfolio Optimization: Implications for Islamic Financial Governance
Keywords:
Diversification Deterministic, Indonesian Islamic Economics, Principles Inclusion - Exclusion, Sharia Portfolio, Union SetsAbstract
This study proposes the application of the Inclusion–Exclusion Principle (PIE) from discrete mathematics as a deterministic framework for optimizing Sharia-compliant investment portfolios in Indonesia. Unlike conventional portfolio optimization approaches that rely on probabilistic models, stochastic simulations, or fuzzy logic, the proposed method utilizes union set operations to integrate various Islamic financial instruments while eliminating asset duplication and overlapping exposures. Using a conceptual and mathematical modeling approach grounded in set theory and the Inclusion–Exclusion Principle, the study constructs an optimal portfolio consisting of sukuk, mudharabah, musyarakah, murabahah, ijarah, and productive waqf assets. The findings indicate that the PIE-based model enhances portfolio diversification by accurately calculating the cardinality of combined asset classes and ensuring that each asset is counted only once within the portfolio structure, thereby improving allocation efficiency, reducing redundancy, and strengthening Sharia compliance through the minimization of hidden overlaps that may create governance concerns. In addition, the model provides a transparent and auditable framework that supports regulatory oversight and Islamic financial governance. Consequently, this study contributes to the expanding literature on Islamic finance by introducing a mathematical governance perspective for portfolio optimization and offers practical implications for regulators and Islamic financial institutions seeking to enhance portfolio management, risk monitoring, and Sharia compliance in an increasingly complex financial environment.
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