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...

We consider the Merton problem with capital gain taxes. Since closed-form solutions are generally unavailable, we provide asymptotic expansions with small interest rate and other parameters, and then obtain an explicit investment and consumption strategy that effectively approximates the optimal...