  The objectives and contributions of this paper are mathematical and numerical
analyses of a stochastic control problem of bounded population dynamics under
ambiguity, an important but not well-studied problem, focusing on the
optimality equation as a nonlinear degenerate parabolic partial
integro-differential equation (PIDE). The ambiguity comes from lack of
knowledge on the continuous and jump noises in the dynamics, and its
optimization appears as nonlinear and nonlocal terms in the PIDE. Assuming a
strong dynamic programming principle for continuous value functions, we
characterize its solutions from both viscosity and distribution viewpoints.
Numerical computation focusing on an ergodic case are presented as well to
complement the mathematical analysis.
