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Value-at-Risk and Models of Dependence in the U.S. Federal Crop Insurance Program

Department of Agricultural and Applied Economics, Virginia Tech, Blacksburg, VA 24061, USA
Department of Economics and Department of Agricultural and Resource Economics, North Carolina State University, Raleigh, NC 27607, USA
Author to whom correspondence should be addressed.
J. Risk Financial Manag. 2019, 12(2), 65;
Received: 29 March 2019 / Revised: 11 April 2019 / Accepted: 15 April 2019 / Published: 16 April 2019
(This article belongs to the Special Issue Risk Analysis and Portfolio Modelling)
PDF [38501 KB, uploaded 16 April 2019]


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. View Full-Text
Keywords: crop insurance; value-at-risk; dependence; copulas; rearrangement algorithm crop insurance; value-at-risk; dependence; copulas; rearrangement algorithm

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Ramsey, A.F.; Goodwin, B.K. Value-at-Risk and Models of Dependence in the U.S. Federal Crop Insurance Program. J. Risk Financial Manag. 2019, 12, 65.

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J. Risk Financial Manag. EISSN 1911-8074 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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