31 citations · 152 across the 38 of their papers we have counts for
4 papers · 1 filter
Uniform error estimates for artificial neural network approximations for heat equations
Lukas Gonon, Philipp Grohs, Arnulf Jentzen +2
Recently, artificial neural networks (ANNs) in conjunction with stochastic gradient descent optimization methods have been employed to approximately compute solutions of possibly r…
Risk bounds for reservoir computing
Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega
We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error co…
On existence and uniqueness properties for solutions of stochastic fixed point equations
Christian Beck, Lukas Gonon, Martin Hutzenthaler +1
The Feynman-Kac formula implies that every suitable classical solution of a semilinear Kolmogorov partial differential equation (PDE) is also a solution of a certain stochastic fix…
Asset Pricing with General Transaction Costs: Theory and Numerics
Lukas Gonon, Johannes Muhle-Karbe, Xiaofei Shi
We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we pro…