Optimal Timing Of Regime Switching In Optimal Growth Models: A Sobolev Space Approach
This paper analyses the optimal timing of switching between alternative and consecutive regimes in optimal growth models. The authors derive the appropriate necessary conditions for such problems by means of the standard techniques from calculus of variations and some basic properties of Sobolev spaces. Many decision processes arising in economics involve a finite number of discrete changes both in the structure of the system and the objective functional over the course of the planning horizon. This paper presents a proof of the necessary conditions for the optimal timing of the switches between these alternative regimes which are of particular importance.