\textbf{Victor Fedyashov} \newline
\textbf{Title:} Ergodic BSDEs with jumps \newline
\textbf{Abstract:} We study ergodic backward stochastic differential equations (EBSDEs) with jumps, where the forward dynamics are given by a non-autonomous (time-periodic coefficients) Ornstein-Uhlenbeck process with Lévy noise on a separable Hilbert space. We use coupling arguments to establish existence of a solution. We also prove uniqueness of the Markovian solution under certain growth conditions using recurrence of the above mentioned forward SDE. We then give applications of this theory to problems of risk-averse ergodic optimal control.
\newline
\textbf{Ruolong Chen} \newline
\textbf{Title:} tba \newline
\textbf{Abstract:}
\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.
Wei Wei
\newline
Title: "Optimal Switching at Poisson Random Intervention Times"
(joint work with Dr Gechun Liang)
\newline
Abstract: The paper introduces a new class of optimal switching problems, where
the player is allowed to switch at a sequence of exogenous Poisson
arrival times, and the underlying switching system is governed by an
infinite horizon backward stochastic differential equation system. The
value function and the optimal switching strategy are characterized by
the solution of the underlying switching system. In a Markovian setting,
the paper gives a complete description of the structure of switching
regions by means of the comparison principle.
\newline
Julen Rotaetxe
\newline
Title: Applicability of interpolation based finite difference method to problems in finance
\newline
Abstract:
I will present the joint work with Christoph Reisinger on
the applicability of a numerical scheme relying on finite differences
and monotone interpolation to discretize linear and non-linear diffusion
equations. We propose suitable transformations to the process modeling
the underlying variable in order to overcome issues stemming from the
width of the stencil near the boundaries of the discrete spatial domain.
Numerical results would be given for typical diffusion models used in
finance in both the linear and non-linear setting.