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Because the distributions of crop yields, prices, and revenues generally are skewed, and because the payoffs from crop insurance and put options follow censored distributions, there is no reason to expect that crop producers' incomes approach the normality needed to justify mean-variance analysis. Numerical integration is used in this paper to approximate crop revenue distributions in their entirety so that various measures of riskiness can be applied. Procedures for finding approximately optimal futures and options hedges with and without crop insurance are described. The results demonstrate that combinations of crop insurance and forward pricing are much more effective than either alone in reducing risks.


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