2014/09/04 by Francesco Bartaloni, Bartaloni, Francesco
Economics, Econometrics and Finance · Mathematics · #Economic Growth and Productivity #Economic theories and models #FOS: Mathematics #Monetary Policy and Economic Impact #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.1409.1288
arxiv created 2014/09/04 · openalex publication_date 2014/09/04 · arxiv updated 2014/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an optimal control problem arising in the context of economic theory of growth, on the lines of the works by Skiba (1978) and Askenazy - Le Van (1999). The economic framework of the model is intertemporal infinite horizon utility maximization. The dynamics involves a state variable representing total endowment of the social planner or average capital of the representative dynasty. From the mathematical viewpoint, the main features of the model are the following: (i) the dynamics is an increasing, unbounded and not globally concave function of the state; (ii) the state variable is subject to a static constraint; (iii) the admissible controls are merely locally integrable in the right half-line. Such assumptions seem to be weaker than those appearing in most of the existing literature. We give a direct proof of the existence of an optimal control for any initial value of the state variable and we carry on a qualitative study of the value function; moreover, using dynamic programming methods, we show that the value function is a continuous viscosity solution of the associated Hamilton-Jacobi-Bellman equation.