The Dynamic Programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE’s with age structure that have been studied in various papers (see e.g. [11, 12], [30, 32]) either in cases when explicit solutions can be found or using Maximum Principle techniques. The problem i...

The theory of optimum economic growth has centred around the 1928 paper of Ramsey and extensively developed by subsequent authors. Samuelson and Solow extended Ramsey's analysis to a world involving multiple capital goods. Following Ramsey's formulation of his problem in terms of constrained maximization of an integral over infinite time, Tinbergen, Koopmans, Cass, Weizacker and Mirrlees worked...

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where X(t) is a controlled jump diffusion and u(t) is the control process. We allow for the case where the controller only has access to partial-information. Thus, we have a infinite horizon problem with partial information. Infinitehorizon optimal control problems arise in many fields of economics, in particular in models of economic growth. Note that because of the general nature of the parti...

We propose a set oriented approach to the global infinite horizon optimal control of nonlinear systems with quantized state measurement and quantized control values. The algorithm relies on a dynamic programming principle in which the quantization error is modelled as an opponent in a min-max dynamic game formulation. For the solution of the problem we propose a set oriented approach followed b...

We consider a portfolio optimization problem which is formulated as a stochastic control problem. Risky asset prices obey a logarithmic Brownian motion, and interest rates vary according to an ergodic Markov diffusion process. The goal is to choose optimal investment and consumption policies to maximize the infinite horizon expected discounted HARA utility of consumption. A dynamic programming ...