SPA Seminar: Controlled measure-valued martingales: a viscosity solution approach

Abstract: We consider a class of stochastic control problems where the state process is a probability measure-valued process satisfying an additional martingale condition on its dynamics, called measure-valued martingales (MVMs). We establish the ‘classical’ results of stochastic control for these problems: specifically, we show that the value function for the problem can be characterised as the unique solution to a Hamilton-Jacobi-Bellman equation in the sense of viscosity solutions. We also illustrate how problems of this type arise in a number of applications. In particular, specific emphasis will be placed on illustrating the connections to Bayesian adaptive control and how these results can be used to adress Bayesian search problems. The talk is based on joint work with Alex Cox, Martin Larsson, Sara Svaluto and Chaorui Wang.

This is a seminar in our seminar series on Stochastic Pocesses and Applications (SPA).