  In this paper, motivated by a problem in stochastic impulse control theory,
we aim to study solutions to a free boundary problem of obstacle-type. We
obtain sharp estimates for the solution using nonlinear tools which are
independent of the modulus of semi-convexity of the obstacle. This allows us to
state a general estimate for solutions to free boundary problems of
obstacle-type admitting obstacles with a general modulus of semi-convexity. As
an application we prove sharp estimates for the solution to a fully nonlinear
stochastic impulse control problem.
