2008/06/26 by Silvia Faggian, Faggian, Silvia, Fausto Gozzi +1
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #35B37 #49J20 #49J27 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.AP #math.OC #msc:35B37 #msc:49J20 #msc:49J27
paper · pdf · doi:10.48550/arxiv.0806.4278
31 pages
arxiv created 2008/06/26 · openalex publication_date 2008/06/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the associated stationary Hamilton--Jacobi--Bellman equation and use this to prove existence and uniqueness of feedback controls. The idea of studying this kind of problem comes from economic applications, in particular from models of optimal investment with vintage capital. Such family of problems has already been studied in the finite horizon case by Faggian. The infinite horizon case is more difficult to treat and it is more interesting from the point of view of economic applications, where what mainly matters is the behavior of optimal trajectories and controls in the long run. The study of infinite horizon is here performed through a nontrivial limiting procedure from the corresponding finite horizon problem.