Many finance problems can be formulated as a singular stochastic control problem, where the associated Hamilton-Jacobi-Bellman (HJB) equation takes the form of variational inequality and its penalty approximation equation is linked to a regular control problem. The penalty method, as a finite...

In this paper, we derive a parabolic variational inequality with double time-like variables from a continuous exercise model of American call options proposed in Rogers and Schienkman (2007). Using viscosity approach, we prove that the value function is a unique viscosity solution to the...