A constrained non-linear regular-singular stochastic control problem, with applications

This paper investigates a mixed regular-singular stochastic control problem where the drift of the dynamics is quadratic in the regular control variable. More importantly, the regular control variable is constrained. The value function of the problem is derived in closed form via solving the corresponding constrained Hamilton–Jacobi–Bellman equation, and optimal controls are obtained explicitly. Applications and economic interpretations of the general results to two applied problems, from which the mathematical problem was originated, are discussed.