Abstract
The federal crop insurance program covered more than 110 billion dollars in total liability in 2018. The program consists of policies across a wide range of crops, plans, and locations. Weather and other latent variables induce dependence among components of the portfolio. Computing value-at-risk (VaR) is important because the Standard Reinsurance Agreement (SRA) allows for a portion of the risk to be transferred to the federal government. Further, the international reinsurance industry is extensively involved in risk sharing arrangements with U.S. crop insurers. VaR is an important measure of the risk of an insurance portfolio. In this context, VaR is typically expressed in terms of probable maximum loss (PML) or as a return period, whereby a loss of certain magnitude is expected to return within a given period of time. Determining bounds on VaR is complicated by the non-homogeneous nature of crop insurance portfolios. We consider several different scenarios for the marginal distributions of losses and provide sharp bounds on VaR using a rearrangement algorithm. Our results are related to alternative measures of portfolio risks based on multivariate distribution functions and alternative copula specifications.
Highlights
The United States federal crop insurance program is one of the largest subsidized agricultural insurance programs in the world
A portion of the actuarially fair premium on the policies is subsidized by taxpayers; for policies with catastrophic coverage the subsidy can be 100 percent of premium but is closer to 60% of premium for the bulk of the policies sold through the program
Policies are priced by the Risk Management Agency (RMA) of the U.S Department of Agriculture (USDA) but are serviced by approved private insurers
Summary
The United States federal crop insurance program is one of the largest subsidized agricultural insurance programs in the world. Policies are priced by the Risk Management Agency (RMA) of the U.S Department of Agriculture (USDA) but are serviced by approved private insurers These insurers are subject to the Standard Reinsurance Agreement (SRA) which controls several aspects of their relationship with the federal government. To develop an aggregate loss distribution for their holdings, the reinsurer is tasked with pooling loss distributions for the underlying insurers This can be challenging for reinsurers handling crop insurance portfolios because of difficulties in separating systemic and pool-able losses (Odening and Shen 2014). By calculating VaR under several different dependence models and deriving sharp bounds using the rearrangement algorithm, we provide estimates of model risk in crop insurance applications. Any top-down approach to loss aggregation should take into account the model risk from dependence in reserving decisions. In either case, using top-down or bottom-up approaches for risk aggregation, the end result is construction of a measure of portfolio risk from marginal risk information
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