Optimal grazing management rules in semi-arid rangelands with uncertain rainfall

We study optimal adaptive grazing management under uncertain rainfall in a discrete-time model. As in each year actual rainfall can be observed during the short rainy season, and grazing management can be adapted accordingly for the growing season, the closed-loop solution of the stochastic optimal control problem does not only depend on the state variable, but also on the realization of the random rainfall. This distinguishes optimal grazing management from the optimal use of most other natural resources under uncertainty, where the closed-loop solution of the stochastic optimal control problem depends only on the state variables. Solving this unusual stochastic optimization problem allows us to critically contribute to a long-standing controversy over how to optimally manage semi-arid rangelands by simple rules of thumb.