The Square-Root Rule for Reinsurance: Further Analysis and Consideration of China’s Market

Abstract

China has been experiencing rapid development in its insurance market in recent years, with its reinsurance market also in a developing stage. Previous theoretical work using a game theory approach suggests that the appropriate number of companies in the insurance market should be the square root of the number of insurers (index = 0.5). To verify the validity of this square-root rule, we conduct an analysis using data over a period. To examine this relationship between the number of insurers and the number of reinsurers, we perform regression analyses using data from the Organization for Economic Cooperation and Development (OECD). We find that the level of the index fluctuates around an index level of 0.4, instead of 0.5, the optimal value by theory. We also observe that this index level fluctuation behaves similar to the price of risk and the property–liability combined ratio. In our analysis, we then replace the number of reinsurers and number of insurers by ceded premium and net premium, respectively, and find similar results. By comparing and calculating these theoretical relationships, we present two formulas of the average size of the reinsurance market with our interpretations on the gap between the theory and the data. In addition, we analyze the Chinese reinsurance market to offer more evidence of our interpretation.