This paper presents farmer’s optimization problem and how it relates to his or her deforestation behavior. The main technique used here is a stochastic control model solved by the Hamilton-Jacobi-Bellman (HJB) equation.

The farmer’s capital accumulation is treated as a jump process approximated by the Poisson process. The control variables are assumed to be of Markovian type. The ARMA(1,1) deforestation model of this paper has given further insight into farmers’ deforestation and capital accumulation behavior. Of particular importance is how farmers’ attitude towards risks (and their precautionary motives of saving) affect these behaviors. A risk-taking farmer appears to be more likely to clear a forest than a risk-averting one. The result also shows the case where consumption optimalization may preclude further forest clearing. But given the limitations of the modeling, these results should be seen as only a part of a much more complex deforestation behavior.