Multi-stage optimal control problems with stochastic switching times

This thesis develops a theory for two-stage optimal control problems with a stochastic switching time and applies it to socioeconomic models. A regime switch, occurring at a random time, divides the problem into two stages. The switch timing depends on a hazard rate function, possibly dependent on endogenous variables. Two solution techniques are explored: a backward approach, solving the second stage first, and a vintage-structure approach, solving both stages simultaneously. Featured applications include optimizing lockdown and vaccination strategies in health economics, managing savings and emissions for climate change, and planning marketing and production strategies amid potential disruptions. The research provides insights into decision-making under uncertainty, demonstrating in the practical applications of the developed theoretical framework the importance of an anticipative behaviour rather than a myopic one.