Document Type : Original Research Paper

Authors

• Majid Benvidi ¹
• seyyed mohammadreza Miri Lavasani ²
• ghodratollah emamverdi ³
• Kambiz Peykarjou ²

¹ Department of Economics, Faculty of Management and Economics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

² Department of Management, Faculty of Management and Economics, Islamic Azad University, Science and Research Branch, Tehran, Iran.

³ Department of Economics, Faculty of Economics and Accounting, Islamic Azad University, Central Tehran Branch, Tehran, Iran.

Abstract

BACKGROUND and OBJECTIVES: The capacity to retain underwriting risk and the continuous provision of strategic mechanisms to augment this capacity are fundamentally essential to the operational stability, long-term survival, and financial resilience of insurance institutions. A primary and globally recognized strategy to achieve this structural resilience is executing robust risk transfer policies through ceded (outward) reinsurance operations. Next to an insurer’s intrinsic capital base and shareholders’ equity, ceded reinsurance serves as the predominant and most accessible instrument for creating additional underwriting capacity, elevating solvency margins, and hedging against catastrophic, cumulative, or unexpectedly heavy losses. However, the financial costs associated with purchasing these reinsurance protections—alongside the strategic necessity of ceding a significant portion of potential insurance benefits and premium income to reinsurers to secure their participation in potential losses—constitute a major operational expenditure for direct insurers. This issue is critically important given the specific characteristics, macroeconomic fluctuations, and unique dynamics of the Iranian insurance market, which often operates under constrained external capacities and requires high internal optimization. Consequently, maximizing the productivity of these consumptive expenses to secure optimal returns, minimizing unnecessary premium leakage, and formulating an efficient ceded reinsurance strategy have become vital for the competitive success of insurers. Therefore, this study aims to determine the ceded reinsurance efficiency frontier of Iranian insurers in a rigorous comparative framework over a specified period, directly addressing existing ambiguities regarding the mathematical and practical optimization of outward reinsurance operations.
METHODOLOGY: This research employs a rigorous quantitative approach utilizing advanced Data Envelopment Analysis (DEA) techniques based on critical financial ratios directly linked to cede reinsurance operations. The mathematical model systematically evaluates the operational and technical efficiency of 22 direct Iranian insurers, acting as autonomous Decision-Making Units (DMUs), over four consecutive financial years (spanning 1400 to 1403). The DEA framework utilized incorporates both constant and variable returns to scale assumptions to provide a nuanced understanding of scale efficiencies within the sector. By identifying the fully efficient units that maximize their output-to-input ratios, the optimal ceded reinsurance efficiency frontier is precisely delineated for each respective financial year. Furthermore, the highly fluctuating macroeconomic and market conditions during this specific four-year timeframe necessitated a granular, longitudinal comparative analysis to discover the underlying reasons for shifts within the efficiency frontier over time. Consequently, the operational outcomes and productivity trajectories of each year were comprehensively evaluated and analyzed utilizing the Malmquist Productivity Index (MPI). By meticulously tracking temporal changes in overall efficiency and isolating the contributing factors—specifically distinguishing between technical efficiency changes (the catch-up effect) and technological changes (the frontier shift)—the MPI plays a pivotal role in developing targeted, data-driven strategies to continuously enhance the operational performance of inefficient DMUs.
FINDINGS: Following the precise determination of the mathematical efficiency frontier based on the performance of the fully efficient units of each evaluated year, targeted strategic pathways and corrective optimization solutions for efficiency enhancement were designed and prescribed using the calculated λ (lambda) values. These solutions are presented to establish empirically validated and highly specific benchmarking frameworks for insurance institutions diagnosed with sub-optimal or inefficient outward reinsurance operations. The reference weights, denoted as λ, precisely indicate which peer companies should be emulated to reach the optimal frontier. Additionally, the longitudinal analysis facilitated by the MPI across the evaluated financial periods demonstrated a highly dynamic and frequently shifting efficiency frontier. This observable dynamism is directly attributed to the evolving systemic conditions of the national insurance market, including inflation rates, regulatory adjustments, and variations in domestic retention capacities during the 1400 to 1403 period. The decomposition of the Malmquist index revealed that while some insurers improved their internal processes, the overall industry frontier experienced periods of regression and progression due to external shocks. These dynamic results, synthesized with the customized benchmarking strategies, culminate in the formulation of comprehensive macro-level action plans that can be practically utilized by executives.
CONCLUSION: The outcomes of this study successfully identify and elucidate the optimal ceded reinsurance efficiency frontier for Iranian insurers, while explicitly outlining the strategic interventions required by direct insurers to structurally improve the functional efficiency of these critical risk-transfer operations. In this regard, localized, highly actionable performance improvement strategies have been explicitly extracted based on the λ reference weights derived from the optimally performing benchmark units. Furthermore, the study calculates and presents auxiliary slack variables which precisely quantify the mathematical deficit or surplus within the input and output financial ratios. This slack analysis highlights exact, quantified areas for operational adjustment, such as reducing unnecessary ceded premiums or renegotiating for better commission rates. Finally, the comprehensive analysis of the MPI, carefully contextualized against the specific economic characteristics and systemic challenges of each financial period, provides a robust, evidence-based, and highly functional analytical foundation. This foundation is designed to directly guide the strategic decision-making processes of corporate insurers and enhance the supervisory frameworks of national regulatory bodies, ensuring long-term market stability.

Keywords

• Ceded Reinsurance Efficiency
• Efficiency Frontier
• Data Envelopment Analysis (DEA)
• Financial Ratio-Based Data Envelopment Analysis
• Malmquist Index

Main Subjects

• Risk management in the insurance industry