11 citations · 18 across the 5 of their papers we have counts for
6 papers · 1 filter
On path-dependent multidimensional forward-backward SDEs
Kaitong Hu, Zhenjie Ren, Nizar Touzi
This paper extends the results of Ma, Wu, Zhang, Zhang [11] to the context of path-dependent multidimensional forward-backward stochastic differential equations (FBSDE). By path-de…
Continuous-Time Principal-Agent Problem in Degenerate Systems
Kaitong Hu, Zhenjie Ren, Nizar Touzi
In this paper we present a variational calculus approach to Principal-Agent problem with a lump-sum payment on finite horizon in degenerate stochastic systems, such as filtered par…
Mean-field Langevin System, Optimal Control and Deep Neural Networks
Kaitong Hu, Anna Kazeykina, Zhenjie Ren
In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introd…
Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks
Kaitong Hu, Zhenjie Ren, David Siska +1
Our work is motivated by a desire to study the theoretical underpinning for the convergence of stochastic gradient type algorithms widely used for non-convex learning tasks such as…
Viscosity solutions of path-dependent PDEs with randomized time
Zhenjie Ren, Mauro Rosestolato
We introduce a new definition of viscosity solution to path-dependent partial differential equations, which is a slight modification of the definition introduced in [8]. With the n…
Perron's method for viscosity solutions of semilinear path dependent PDEs
Zhenjie Ren
This paper proves the existence of viscosity solutions of path dependent semilinear PDEs via Perron's method, i.e. via showing that the supremum of viscosity subsolutions is a visc…