Systematic Literature Review: Optimal Stopping and Investment Optimization for Bankruptcy Risk Management in Sharia Insurance

The increasing demand for Sharia-compliant financial services in Muslim-majority countries such as Indonesia has driven the rapid development of Sharia insurance (Takaful). Despite its growth, the Sharia insurance sector faces significant challenges in managing investment portfolios and mitigating bankruptcy risks. Addressing these challenges requires a comprehensive understanding of the existing mathematical and financial models configured according to Islamic principles. Several studies have introduced stochastic approaches to model surplus processes, investment returns, and risk probabilities in insurance operations. Among these, the Cramér–Lundberg model has been widely used to estimate surplus dynamics and bankruptcy risks, while the Vasicek model provides a stochastic framework for modeling investment returns. Quadratic programming has also been applied to optimize asset allocation under specific constraints. However, these methodologies have typically been explored in isolation, which limits their ability to provide an integrated and effective framework for simultaneous bankruptcy risk mitigation and Sharia-compliant investment optimization. This methodological gap constrains the advancement of comprehensive, practically applicable, and theoretically sound solutions that are specifically designed to address the distinctive operational characteristics of Shariainsurance. The objective of this systematic review of the literature is to synthesize and critically analyze the methods used in previous research and to explore how they can be systematically integrated to form a comprehensive risk and investment management framework for Sharia insurance. The review identifies the strengths, limitations, and potential for combining optimal stopping theory, stochastic surplus modeling, and investment optimization to support robust financial decision making. This review contributes by offering a structured research agenda for the development of integrated models that simultaneously address the complexities of bankruptcy risk and Sharia-compliant investment strategies. Furthermore, this study provides valuable information for academics and practitioners seeking to improve the financial sustainability of the Islamic Insurance industry.