On the policy improvement algorithm in continuous time

Puntos clave

• The aim is to develop a new approach to the Policy Improvement Algorithm for stochastic control in continuous-time processes.
• Introduced a general framework for the Policy Improvement Algorithm assuming controls in a compact metric space.
• Established sufficient conditions for the algorithm to be well-defined and to converge in continuous time.
• Provided examples demonstrating the applicability of the algorithm in weak stochastic control contexts.
• The Policy Improvement Algorithm was shown to converge under the established conditions.
• Explicit examples illustrated the necessity of weak formulations in certain control problems.
• Demonstrated effectiveness in diffusion-based classes of problems.