Publications (57)
Pathwise Solutions for Stochastic Hydrostatic Euler Equations under the Local Rayleigh Condition
Ruimeng Hu, Quyuan Lin
The hydrostatic Euler equations are important in the study of atmospheric and oceanic dynamics in the planetary scale. While its deterministic version has been widely studied in th…
Asymptotic Optimal Portfolio in Fast Mean-reverting Stochastic Environments
Ruimeng Hu
This paper studies the portfolio optimization problem when the investor's utility is general and the return and volatility of the risky asset are fast mean-reverting, which are imp…
Deep Fictitious Play for Stochastic Differential Games
Ruimeng Hu
In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms for computing the Nash equilibrium of asy…
Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games
Jiequn Han, Ruimeng Hu
We propose a deep neural network-based algorithm to identify the Markovian Nash equilibrium of general large -player stochastic differential games. Following the idea of fictiti…
Deep Learning for Ranking Response Surfaces with Applications to Optimal Stopping Problems
Ruimeng Hu
In this paper, we propose deep learning algorithms for ranking response surfaces, with applications to optimal stopping problems in financial mathematics. The problem of ranking re…
Regularization by noise for the inviscid primitive equations
Ruimeng Hu, Quyuan Lin, Rongchang Liu
The deterministic inviscid primitive equations (also called the hydrostatic Euler equations) are known to be ill-posed in Sobolev spaces and in Gevrey classes of order strictly gre…