Inferência probabilística para seguro paramétrico

Abstract

The objective of this work was to develop and apply a modeling method for parametric agricultural insurance contracts with coverage for the occurrence of extreme weather events, aiming at determining indemnity triggers with reduced base risk. The proposed method used the generalized distribution of extreme values (GEV) to model extreme weather events and used the exceedance probabilities found for the extreme quantiles as an explanatory variable for a logistic model that predicts crop losses. Bayesian inference was applied to estimate the parameters of the GEV distribution and the coefficients of the logistic model. Subsequently, the accuracy and cost for the insurer and insured for all possible contractual triggers were verified, with the intention of providing a technical basis for the contract manager to identify the safest trigger and with viable costs for the product. After presenting the method, a case study was carried out aiming at its application for the elaboration of a contract for the protection of coffee plantations against the occurrence of extreme dry spells during the flowering period in some cities of the State of Minas Gerais. Two models were fitted, one with an informative a priori distribution for estimating the parameters of the GEV distributions and the other with a non-informative a priori distribution. The results found were promising. The proposed model showed 87.5% accuracy for the two a priori distribution structures when relating the weather event to the occurrence of crop losses, even in a scenario of scarce data. In addition, with the informative a priori use, it was possible to find an optimal trigger to relate the climatic event and the occurrence of losses and that brought a viable cost of commercialization for both agents involved. The use of the Bayesian inferential approach made it possible, through credibility intervals, for the uncertainty of the process to be quantified with reasonable precision in all stages of the modeling, providing a greater degree of basis for the contract managers to make decisions. It is concluded that the method proposed here proved to be promising and can be adapted for contracts of different cultures and climatic events.