Chiara Segala

Michael Multerer, Paul Schneider, Chiara Segala

We propose a scalable and theoretically grounded low-rank conditional expectation model for recursive Monte Carlo optimal stopping problems, in particular American option pricing. Our method reformulates the estimation of continuation values as a learning problem in a reproducing kernel Hilbert space, in which the conditional expectation is represented as a linear operator acting on future payoffs. This perspective yields an offline-online decomposition: the operator is learned once from simulated data and subsequently reused across all exercise dates, eliminating the need to recompute regression models at each step of the backward recursion. We establish convergence guarantees and derive bounds quantifying the approximation errors across exercise dates. Numerical experiments demonstrate the speed and accuracy of the proposed approach relative to extant methods.

Giacomo Albi, Sara Bicego, Michael Herty et al.

Feedback control synthesis for large-scale particle systems is reviewed in the framework of model predictive control (MPC). The high-dimensional character of collective dynamics hampers the performance of traditional MPC algorithms based on fast online dynamic optimization at every time step. Two alternatives to MPC are proposed. First, the use of supervised learning techniques for the offline approximation of optimal feedback laws is discussed. Then, a procedure based on sequential linearization of the dynamics based on macroscopic quantities of the particle ensemble is reviewed. Both approaches circumvent the online solution of optimal control problems enabling fast, real-time, feedback synthesis for large-scale particle systems. Numerical experiments assess the performance of the proposed algorithms.