An exact viscosity solution to a Hamilton–Jacobi–Bellman quasi-variational inequality for animal population management

Abstract

Abstract We formulate a stochastic impulse control model for animal population management and a candidate of exact solutions to a Hamilton–Jacobi–Bellman quasi-variational inequality. This model has a qualitatively different functional form of the performance index from the existing monotone ones. So far, optimality and unique solvability of the Hamilton–Jacobi–Bellman quasi-variational inequality has not been investigated, which are thus addressed in this paper. We present a candidate of exact solutions to the Hamilton–Jacobi–Bellman quasi-variational inequality and prove its optimality and unique solvability within a certain class of solutions in a viscosity sense. We also present and examine a dynamical system-based numerical method for computing coefficients in the exact solutions.

Keywords

• Population management
• Threshold control
• Hamilton–Jacobi–Bellman quasi-variational inequalities
• Viscosity solution
• Feeding damage
• Uniqueness and existence of solution