\textbf{James Newbury} \newline
Title: Heavy traffic diffusion approximation of the limit order book in a one-sided reduced-form model. \newline
Abstract: Motivated by a zero-intelligence approach, we try to capture the
dynamics of the best bid (or best ask) queue in a heavy traffic setting,
i.e when orders and cancellations are submitted at very high frequency.
We first prove the weak convergence of the discrete-space best bid/ask
queue to a jump-diffusion process. We then identify the limiting process
as a regenerative elastic Brownian motion with drift and random jumps to
the origin.
\newline
\textbf{Zhaoxu Hou} \newline
Title: Robust Framework In Finance: Martingale Optimal Transport and
Robust Hedging For Multiple Marginals In Continuous Time
\newline
Abstract: It is proved by Dolinsky and Soner that there is no duality
gap between the robust hedging of path-dependent European Options and a
martingale optimal problem for one marginal case. Motivated by their
work and Mykland's idea of adding a prediction set of paths (i.e.
super-replication of a contingent claim only required for paths falling
in the prediction set), we try to achieve the same type of duality
result in the setting of multiple marginals and a path constraint.