A portfolio optimization model combining pooling and group buying of reinsurance under an asset liability management approach
Porth, Lysa M.
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Some insurance firms are faced with the unique challenge of managing risks that are large, infrequent, and potentially highly correlated within geographic regions and/or across product lines. An example of this is crop insurance, which includes weather risk, and leads to a portfolio of risks with high variance. A solution to this problem is undertaken in this study, through using a combination of pooling and private reinsurance in a portfolio approach. This approach takes advantage of offsetting risks across regions, in order to reduce risk in a cost effective manner. An asset liability management (ALM) approach is used to examine the entire crop insurance sector for Canada. This is the first study to focus on pooling for an entire insurance sector in a country, and it uses all major crops from 1978-2009, across 10 regions (provinces). Chapter two develops an innovative insurance portfolio under a full premium pool, combining a self managed insurance pool and private reinsurance using the coefficient of variation (CV) of the loss coverage ratio (LCR), Model 3. Results show that this portfolio approach reduces risk across regions. Chapter three, in contrast to chapter two, uses a reinsurance premium pool, where regions contribute only a portion of their risk to a reinsurance pool. An improved insurance portfolio model is developed in chapter three, using combinatorial optimization with a genetic algorithm to combine a self managed reinsurance pool and private reinsurance, Model C. Results show that this reinsurance portfolio model efficiently reduces risk. Chapter four uses a similar approach to chapter three, except that it allows for dependence (correlation) across regions. Results for this model (Model CC) are consistent with those of chapter three, indicating the effectiveness of the portfolio approach when correlation is present across regions. Overall, the portfolio models developed in each of the three chapters (Model 1, Model C, and Model CC), produce acceptable surplus, survival probability, and deficit at ruin, indicating that the portfolio approach using pooling is efficient for reducing risk. Beyond crop insurance, the portfolio models can be applied to other large natural disaster and weather related insurance, and other portfolio applications.