Abstract
In this paper, we focus on the farmer's risk income, by using commodity futures, when price and output processes are correlated random represented by jump-diffusion models. We evaluate the expected utility of the farmer's wealth and we determine, at each instant of time, the optimal consumption rate and hedge position at given the time to harvest and state variables. We find a closed form optimal position of consumption and position rate in case of CARA utility investor. This result (see table 1.5) is a generalization of Ho (1984) result who consider the particular case where price and output are diffusion models.