13 citations · 39 across the 18 of their papers we have counts for
22 papers
Stable Allocations, Unstable Payment Paths: The Shapley Value and Voluntary Coalition Formation
Tongseok Lim
The random-order interpretation of the Shapley value specifies both a terminal allocation and a payment path: each entrant is paid her marginal contribution at the time of entry. W…
Node classification in networks via simplicial interactions
Eunho Koo, Tongseok Lim
In the node classification task, it is natural to presume that densely connected nodes tend to exhibit similar attributes. Given this, it is crucial to first define what constitute…
Replication of financial derivatives under extreme market models given marginals
Tongseok Lim
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretica…
Maximal monotonicity and cyclic involutivity of multi-conjugate convex functions
Tongseok Lim
A cornerstone in convex analysis is the crucial relationship between functions and their convex conjugate via the Fenchel-Young inequality. In this dual variable setting, the maxim…
Cooperative networks and Hodge-Shapley value
Tongseok Lim
Lloyd Shapley's cooperative value allocation theory stands as a central concept in game theory, extensively utilized across various domains to distribute resources, evaluate indivi…
Classifying minimum energy states for interacting particles: Regular simplices
Cameron Davies, Tongseok Lim, Robert J. McCann
Densities of particles on $\Rn$ which interact pairwise through an attractive-repulsive power-law potential $W_{\al,\bt}(x) = |x|^\al/\al-|x|^\bt/\bt$ have often been used to expla…
Classifying minimum energy states for interacting particles: Spherical Shells
Cameron Davies, Tongseok Lim, Robert J. McCann
Particles interacting through long-range attraction and short-range repulsion given by power-laws have been widely used to model physical and biological systems, and to predict or…
Hodge theoretic reward allocation for generalized cooperative games on graphs
Tongseok Lim
This paper generalizes L.S. Shapley's celebrated value allocation theory on coalition games by discovering and applying a fundamental connection between stochastic path integration…
Axiomatic and Probabilistic Foundations for the Hodge-Theoretic Shapley Value
Tongseok Lim
This paper establishes a complete theoretical foundation for the Hodge-theoretic extension of the Shapley value introduced by Stern and Tettenhorst (2019). We show that a set of fi…
On the cardinality of sets in obeying a slightly obtuse angle bound
Tongseok Lim, Robert J. McCann
In this paper we explicitly estimate the number of points in a subset as a function of the maximum angle that any three of these points form, provided…
Maximizing expected powers of the angle between pairs of points in projective space
Tongseok Lim, Robert J. McCann
Among probability measures on -dimensional real projective space, one which maximizes the expected angle between independently drawn…
On Fejes Tóth's conjectured maximizer for the sum of angles between lines
Tongseok Lim, Robert J. McCann
Choose unoriented lines through the origin of . The sum of the angles between these lines is conjectured to be maximized if the lines are distributed as evenly a…
Geometrical bounds for the variance and recentered moments
Tongseok Lim, Robert J. McCann
We bound the variance and other moments of a random vector based on the range of its realizations, thus generalizing inequalities of Popoviciu (1935) and Bhatia and Davis (2000) co…
Robust pricing and hedging of options on multiple assets and its numerics
Stephan Eckstein, Gaoyue Guo, Tongseok Lim +1
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-margin…
Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials
Kyungkeun Kang, Hwa Kil Kim, Tongseok Lim +1
In this paper, we are concerned with local minimizers of an interaction energy governed by repulsive-attractive potentials of power-law type in one dimension. We prove that sum of…
Isodiametry, variance, and regular simplices from particle interactions
Tongseok Lim, Robert J McCann
Consider a collection of particles interacting through an attractive-repulsive potential given as a difference of power laws and normalized so that its unique minimum occurs at uni…
Optimal Brownian stopping when the source and target are radially symmetric distributions
Nassif Ghoussoub, Young-Heon Kim, Tongseok Lim
Given two probability measures on , in subharmonic order, we describe optimal stopping times that maximize/minimize the cost functional $\mathbb{E} |B_0 -…
Optimal Brownian Stopping between radially symmetric marginals in general dimensions
Nassif Ghoussoub, Young-Heon Kim, Tongseok Lim
Given an initial (resp., terminal) probability measure (resp., ) on , we characterize those optimal stopping times that maximize or minimize the functional…
Dual attainment for the martingale transport problem
Mathias Beiglboeck, Tongseok Lim, Jan Obłój
We investigate existence of dual optimizers in one-dimensional martingale optimal transport problems. While [BNT16] established such existence for weak (quasi-sure) duality, [BHP13…
Geometry of vectorial martingale optimal transportations and duality
Tongseok Lim
The theory of Optimal Transport (OT) and Martingale Optimal Transport (MOT) were inspired by problems in economics and finance and have flourished over the past decades, making sig…
Structure of optimal martingale transport plans in general dimensions
Nassif Ghoussoub, Young-Heon Kim, Tongseok Lim
Given two probability measures and in "convex order" on , we study the profile of one-step martingale plans on that optimize the expected value…
Optimal martingale transport between radially symmetric marginals in general dimensions
Tongseok Lim
We determine the optimal structure of couplings for the \emph{Martingale transport problem} between radially symmetric initial and terminal laws on and show the uniqu…