Applications of dynamic programming to economic problems with vintage capital

This is the second of two papers on boundary optimal control problems with linear state equation and convex cost arising in Economics and the the associated Hamilton-Jacobi-Bellman equation. In the ¯rst paper we studied existence and uniqueness of the solution of HJB in strong sense, namely the pointwise limit of classical solutions of approximating equations, which proves to be also Lipschitz in time and regular in the state variable. In this second paper we apply Dynamic Programming to show that the value function of the economic problem is the unique strong solution of the associated HJB equation.