In this study we develop a new methodological proposal to incorporate risk into a farm‐level positive mathematical programming (PMP) model. We estimate simultaneously the farm nonlinear cost function and a farmer‐specific coefficient of absolute risk aversion as well as the resource shadow prices. The model is applied to a sample of representative arable crop farms from the Emilia‐Romagna region in Italy. The estimation results confirm the calibration ability of the model and reveal the values of the individual risk aversion coefficients. We use the model to simulate different scenarios of crop price volatility, in order to explore the potential risk management role of an agri‐environmental scheme.