Abstracts > Higuera Chan Carmen Geraldi

Joint work with Leonardo R. Laura-Guarachi, Adolfo Minjárez-Sosa

We present a class of stochastic optimal control problems whose dynamics are governed by success-runs Markov chains. Our analysis combines tools from ergodic theory, dissipativity, and long-run optimal control. We characterize stationary state-control pairs and identify structural properties that play a central role in the solution of the associated optimization problems. Furthermore, we derive an explicit storage function that allows us to establish dissipativity and stability properties of the underlying dynamics.

As an application, we study a stochastic forest management model involving a large population of trees subject to random mortality. By means of a mean-field approximation, we obtain an equivalent deterministic control problem whose optimal policy can be characterized through stationary distributions. This framework provides a tractable approach for analyzing large-scale stochastic systems and their long-run behavior.