Chair: Dr Ajay Chandra
15:00 – 15:20
Dr Yonatan Shadmi
Fluid-Limits of Fragmented Limit-Order Markets
Maglaras, Moallemi, and Zheng (2021) have introduced a flexible queueing model for fragmented limit-order markets, whose fluid limit remains remarkably tractable. In this talk we show that, in the limit of small and frequent orders, the discrete system indeed converges to the fluid limit, which is characterized by a system of coupled nonlinear ODEs with singular coefficients at the origin. Moreover, we establish that the fluid system is asymptotically stable for an arbitrary number of limit order books in that, over time, it converges to the stationary equilibrium state studied by Maglaras et al. (2021).
15:20 – 15:40
Dr Eyal Neumann
Stochastic Games with Heterogeneous Players and their Graphon Scaling Limits
We consider a general class of finite-player stochastic games on graphs with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on the controls. We propose a novel approach for deriving the Nash equilibrium of the game semi-explicitly in terms of operator resolvents, by reducing the associated first order conditions to a system of stochastic Fredholm equations of the second kind and deriving their solution in semi-explicit form.
Furthermore, by proving stability results for the system of stochastic Fredholm equations, we derive the convergence of the equilibrium of the N-player games on dense graphs to the corresponding infinite-dimensional graphon game.
Finally, we apply our general framework to solve various examples, such as stochastic Volterra linear-quadratic games, models of systemic risk and advertising with delay, and optimal liquidation games with transient price impact.
15:40 – 16:00
Prof Dan Crisan
The identification of diffusions from imperfect observations
I will present some results related to the identification of a diffusion process X when a running function of it, say h(X) is observed. A point-wise observation of the process (in other words, observing h(X) in isolation cannot identify X unless the function h is injective. However observing h(X) on a small interval [t,t+a] can be enough to determine X exactly.
The paper contain results that expand on this idea; in particular, a property of `fine total asymmetry’ of twice continuously differentiable h is introduced that depends on the fine topology of potential theory and that is both necessary and sufficient for X to be adapted to a natural right-continuous filtration generated by the observations. This particular filtration, though augmented with null sets, does not depend on the initial distribution of X. For real-analytic h the property reduces to simple asymmetry.
The talk is based on joint work with Martin Clark.
16:00 – 16:20
COFFEE BREAK
16:20 – 16:40
Dr Robin Ryder
Coupling MCMC algorithms on submanifolds
We develop MCMC couplings for the special case of a distribution taking values on a submanifold of an ambient space. We demonstrate the efficiency of this approach, and show how to extend these ideas to generic sampling problems.
Work in progress, joint with Elena Bortolato (Pompeu Fabra) and Pierre Jacob (ESSEC).”
16:40 – 17:00
Dr Daniel Heydecker
Dynamic Large Deviations: In search of matching bounds
We discuss the dynamical large deviations of three models: Kac’s model of the Boltzmann Equation, a rescaled zero-range process converging to the porous medium equation, and the Landau-Lifschitz-Navier-Stokes equations. For these models, we discuss the challenges and successes of finding matching bounds, the links to well- or ill-posedness in low regularity classes, and the connection to the equality case of classical inequalities.