Reducing Risk Through Pooling and Selective Reinsurance Using Simulated Annealing: An Example from Crop Insurance

Agricultural insurance is often faced with the challenge of systemic risk, arising from weather risks that tend to be correlated within a specific region in extreme situations, resulting in large crop losses within the region. However, across many regions, especially if regions are considerable distances apart, weather may be quite different and losses may be much less correlated. The objective of this paper is to improve the diversification of a crop insurance portfolio, through developing a new alternative risk management approach (Model 3) that pools crop risks across all provinces in a country to form a Canada-wide joint insurance pool. This is in contrast to the current approach used in Canada, where crop risks are pooled only within an individual province. Then using a simulated annealing optimization approach, the most suitable combination of the 150 crop types in the portfolio is identified for either retaining in the joint insurance pool or for ceding to reinsurers, such that the variance of the loss coverage ratio of the portfolio is minimized. This model overcomes the problem of insufficient diversification that makes pooling of systemic weather risk challenging. It achieves diversification at a lower cost by using a more efficient combination of pooling and selective reinsurance, resulting in overall higher surplus, higher survival probability, and lower deficit at ruin.