  This work focuses on optimal harvesting-renewing for a stochastic population.
A mixed regular-singular control formulation with a state constraint and
regime-switching is introduced. The decision-makers either harvest or renew
with finite or infinite harvesting/renewing rates. The payoff functions depend
on the harvesting/renewing rates. Several properties of the value functions are
established. The limiting value function as the white noise intensity
approaches infinity is identified. The Markov chain approximation method is
used to find a numerical approximation of the value function and optimal
strategies.
