Dejan Siraj (University of Warwick)

Title: Mirror and Synchronous Couplings of Geometric Brownian Motions

Abstract: First we study the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We prove that in the case of the infinite time horizon and ergodic average criteria, the two couplings are always optimal. On the other hand, we show that this is not necessarily true for the finite time horizon problem and present a characterisation of when exactly the optimality of the two couplings fails. When this is the case, we then try to use the policy improvement algorithm to describe the solution. Based on joint work with Saul D. Jacka and Aleksandar Mijatovic.