In this paper the dynamic programming approach is exploited in order to identify the closed loop policy function, and the consumption smoothing mechanisms in an endogenous growth model with time to build, linear technology and irreversibility constraint in investment. Moreover the link among the...

In this paper a family of optimal control problems for economic models is considered, whose state variables are driven by Delay Differential Equations (DDE's). Two main examples are illustrated: an AK model with vintage capital and an advertising model with delay e ect. These problems are very...

A family of economic and demographic models governed by linear delay differential equations is considered. They can be expressed as optimal control problems subject to delay differential equations (DDEs) characterized by some non-trivial mathematical difficulties: state/control constraints and...

We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial differential equations. We introduce and prove a verification theorem which provides a sufficient condition for optimality. Moreover we prove...

We present an application of the Dynamic Programming (DP) and of the Maximum Principle (MP) to solve an optimization over time when the production function is linear in the stock of capital (Ak model). Two views of capital are considered. In one, which is embraced by the great majority of...

Economic and demographic models governed by linear delay differential equations are expressed as optimal control problems in infinite dimensions. A general objective function is considered and the concavity of the Hamiltonian is not required. The value function is a viscosity solution of the...

We present a growth model in which a non-renewable resource enters in the production function. The non-renewable resource is supposed to be sold by an external monopolistic that maximizes his intertemporal discounted cash flow. This approach allows to endogenize the price of the resource. We use...

We present an Hilbert space formulation for a set of implied volatility models introduced in \cite{BraceGoldys01} in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price $T$ an $K$, to be arbitrage free. The arbitrage free...

This paper deals with an endogenous growth model with vintage capital and, more precisely, with the AK model proposed in [18]. In endogenous growth models the introduction of vintage capital allows to explain some growth facts but strongly increases the mathematical difficulties. So far, in this...

This paper extends the standard neoclassical model by considering a technology sector through which an economy with limited human capital attempts to catch up with a given "locomotive" pushing exogenously technical progress. In periods of technological stagnation, economies close enough to the...