Optimal dynamic provision in continuous time

We are interested in the following model: A principal privately observes the evolution of a continuous-time Markov chain and sends messages over time to an agent. The current payoff of the agent depends only on his action and on the current state of the process, while the payoff of the principal depends only on the action of the agent. The analogue discrete time model was studied by Renault-Solan-Vieille (2017) (see also Ely (2017)). They focus on the problem in small dimensions and show that there is no simple universally optimal strategy for the principal. The same holds in continuous time. However, it is possible to characterize the  optimal payoff of the principal as a solution of a PDE as well as the solution of a control problem over pure jump Markov processes.  A verification theorem permits to solve explicitly several examples.

The talk is based on a joint work with Fabien Gensbittel from ESC Toulouse.