Necessary conditions for infinite-horizon discounted two-stage optimal control problems (Q5941453)

In many situations in Economics, one would like to analyse the optimal timing of switching between alternative and consecutive regimes. A natural framework for such an analysis seems to be one of multi-stage optimal control problems, where the switching instants between regimes are endogenously determined. The existing literature considers only the case of two-stage optimal control problems with finite horizon. However, in many cases, it seems more appropriate to consider a problem with an infinite horizon. By deriving the appropriate necessary conditions for such a problem we generalise the methodology in analysing endogenous regime switches.