16 citations · 30 across the 11 of their papers we have counts for
13 papers
Semi-discrete quadratic Wasserstein energy and state-dependent Langevin exploration
Ran Gu, Gaoyue Guo, Kelvin Shuangjian Zhang
We study the semi-discrete quadratic Wasserstein energy. The energy is nonsmooth at collisions of sites. We prove local Lipschitz continuity on the full configuration space, togeth…
An inverse problem in optimal transport on closed Riemannian manifolds
Jian Zhai, Kelvin Shuangjian Zhang
We consider the problem of recovering the Riemannian metric on a compact closed manifold from the optimal transport maps when the underlying cost function is the squared Riemann di…
The monopolist's free boundary problem in the plane
Robert J. McCann, Cale Rankin, Kelvin Shuangjian Zhang
We study the Monopolist's problem with a focus on the free boundary separating bunched from unbunched consumers, especially in the plane, and give a full description of its solutio…
Bumpy metric theorem for co-rank 1 sub-Riemannian and reversible sub-Finsler metrics
Shahriar Aslani, Ke Zhang
We prove that for a generic sub-Riemannian and reversible sub-Finsler metrics defined on a fixed co-rank 1 distribution, all strictly normal periodic orbits are non-degenerate.
Comment on "Ironing, sweeping, and multidimensional screening''
Robert J. McCann, Kelvin Shuangjian Zhang
In their study of price discrimination for a monopolist selling heterogeneous products to consumers having private information about their own multidimensional types, Rochet and Ch…
regularity for principal-agent problems
Robert J. McCann, Cale Rankin, Kelvin Shuangjian Zhang
We prove the interior regularity of the indirect utilities which solve a subclass of principal-agent problems originally considered by Figalli, Kim, and McCann. Our appro…
A duality and free boundary approach to adverse selection
Robert J. McCann, Kelvin Shuangjian Zhang
Adverse selection is a version of the principal-agent problem that includes monopolist nonlinear pricing, where a monopolist with known costs seeks a profit-maximizing price menu f…
Bounds on Choquet Risk Measures in Finite Product Spaces with Ambiguous Marginals
Mario Ghossoub, David Saunders, Kelvin Shuangjian Zhang
We investigate the problem of finding upper and lower bounds for a Choquet risk measure of a nonlinear function of two risk factors, when the marginal distributions of the risk fac…
Wasserstein Control of Mirror Langevin Monte Carlo
Kelvin Shuangjian Zhang, Gabriel Peyré, Jalal Fadili +1
Discretized Langevin diffusions are efficient Monte Carlo methods for sampling from high dimensional target densities that are log-Lipschitz-smooth and (strongly) log-concave. In p…
Existence of solutions to principal-agent problems with adverse selection under minimal assumptions
Guillaume Carlier, Kelvin Shuangjian Zhang
We prove an existence result for the principal-agent problem with adverse selection under general assumptions on preferences and allocation spaces. Instead of assuming that the all…
Implicit Manifold Learning on Generative Adversarial Networks
Kry Yik Chau Lui, Yanshuai Cao, Maxime Gazeau +1
This paper raises an implicit manifold learning perspective in Generative Adversarial Networks (GANs), by studying how the support of the learned distribution, modelled as a subman…
Existence in Multidimensional Screening with General Nonlinear Preferences
Kelvin Shuangjian Zhang
We generalize the approach of Carlier (2001) and provide an existence proof for the multidimensional screening problem with general nonlinear preferences. We first formulate the pr…
On concavity of the monopolist's problem facing consumers with nonlinear price preferences
Robert J. McCann, Kelvin Shuangjian Zhang
A monopolist wishes to maximize her profits by finding an optimal price policy. After she announces a menu of products and prices, each agent will choose to buy that product $y…