Mathematical Modeling for Estimating the Risk of Rice Farmers’ Losses Due to Weather Changes

Abstract

This paper discusses the relationship between weather and rice productivity modeled using the Cobb–Douglas production function principle, with the hypothesis that rice production will increase in line with the increase in average rainfall, wind speed, and temperature every month and then decrease if the weather conditions exceed the threshold. As a result, farmers have the risk of losing rice production. To overcome this problem, we try to estimate the value of the risk. The purpose of this study is to estimate the risk of losses that occurred in rice plants due to weather changes. The method used in this study is risk estimation with the Tail Value at Risk (TVaR) approach. In addition to TVaR, it is estimated simultaneously with Value at Risk (VaR) and Conditional Value at Risk (CVaR). This study uses weather data consisting of rainfall data, wind speed, and air temperature collected from geophysical and meteorological data. Meanwhile, yield data were obtained and processed from the Central Statistics Agency and the West Java Agricultural Service. The data used are data from 2008 to 2021. There are two main parts of the results in this study, namely mathematical analysis and data analysis. The mathematical analysis is a risk model derivation process, which includes TVaR risk measurement. The data analysis process is a simulation of the estimated risk of rice production loss. The results obtained from this study are the value of opportunity risk of loss based on the VaR, CVaR, and TVaR approaches. The conclusion of this study is that the rice plants have a risk of loss in the form of reduced yields caused by weather changes. Farmers can plan to overcome this loss problem, by setting up a reserve fund. Risk of loss can be managed through the rice agricultural insurance program. This is in line with the Indonesian government’s program through the ministry of agriculture. Thus, farmers, insurance companies, and the government can manage the risk of losing rice yields.