Unique solvability of a singular stochastic control model for population management

We present and mathematically analyze a singular stochastic control model for cost-effective and ecologically-sound indirect population control strategy for fish-eating birds. Finding the optimal strategy of a threshold type reduces to solving a variational inequality. We prove the unique existence of its viscosity solution that is neither convex nor concave, which turns out to be a classical solution. Comparative statics on the optimal threshold is performed as well to demonstrate practical implications of the model.