Using Age Structure for a Multi-stage Optimal Control Model with Random Switching Time

The paper presents a transformation of a multi-stage optimal control model with random switching time to an age-structured optimal control model. Following the mathematical transformation, the advantages of the present approach, as compared to a standard backward approach, are discussed. They relate in particular to a compact and unified representation of the two stages of the model: the applicability of well-known numerical solution methods and the illustration of state and control dynamics. The paper closes with a simple example on a macroeconomic shock, illustrating the workings and advantages of the approach.