Stochastic Optimal Control of Interacting Particle Systems in Hilbert Spaces and Applications in Economics

Optimal control of interacting particles governed by stochastic evolution equations in Hilbert spaces is an open area of research. Such systems naturally arise in formulations where each particle is modeled by stochastic partial differential equations, path-dependent stochastic differential equations (such as stochastic delay differential equations or stochastic Volterra integral equations), or partially observed stochastic systems. In this talk we present a limiting theory as the number of particles tends to infinity. We apply the developed theory to problems arising in economics where the particles are modeled by stochastic partial differential equations and stochastic delay differential equations.

The talks is based on [F. de Feo, F. Gozzi, A. Swiech, L. Wessels, Stochastic Optimal Control of Interacting Particle Systems in Hilbert Spaces and Applications, arXiv preprint arXiv:2511.21646]