In this paper we develop a new methodological proposal to incorporate risk into a farm level Positive Mathematical Programming (PMP) model. Our model presents some innovations with respect to the previous literature and estimates simultaneously the resource shadow prices, the farm non-linear cost function and a farm-specific coefficient of absolute risk aversion. The proposed model has been applied to three farm samples and the estimation results confirm the calibration ability of the model and show values for risk aversion coefficients consistent with the literature. Finally we simulate different scenarios of crop price volatility to test the model reactions as well as the potential role of an agri-environmental scheme as risk management tool.