FRE Special Seminar: Sturmius Tuschmann and Hao Xing
This event is free, but registration is required in order to be given access to Columbia University.
Sturmius Tuschmann (Imperial College London)
Title
A Fredholm Approach to Nonlinear Propagator Models
Abstract
We formulate and solve an optimal trading problem with alpha signals, where transactions induce nonlinear transient price impact described by a general propagator model. In particular, our formulation integrates the well-known square-root law of price impact with the empirical observation that impact decays according to a power law. Using a variational approach, we demonstrate that the optimal trading strategy satisfies a nonlinear stochastic Fredholm equation with both forward and backward coefficients. We prove the existence and uniqueness of the solution under a monotonicity condition reflecting the nonlinearity of the price impact. Moreover, we derive an existence result for the optimal strategy beyond this condition when the underlying probability space is countable. In addition, we introduce a novel iterative scheme and establish its convergence to the optimal trading strategy. Finally, we provide a numerical implementation of the scheme that illustrates its convergence, stability, and the effects of concavity on optimal execution under exponential and power-law decay. This is joint work with Eduardo Abi Jaber, Alessandro Bondi, Nathan De Carvalho, and Eyal Neuman.
Hao Xing (Boston University)
Title
Dynamic Bank Run: a mean-field game perspective
Abstract
We study a dynamic bank run model in which the probability of bank failure rises with the share of depositors who withdraw. Strategic complementarities among depositors give rise to multiple equilibria, including an earliest-run and a latest-run equilibrium. Although equilibrium is generally not unique, uniqueness can be restored among threshold equilibria in the presence of common shocks. Depositors with low idiosyncratic expected payoffs may choose to run collectively, even when their private states differ. The run can occur earlier when a larger fraction of depositors is vulnerable to withdrawal incentives. This is a joint work with Jodi Dianetti, Giorgio Ferrari, and Yunzhi Hu.