Related papers: Risk measures based on weak optimal transport

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-marginal martingale optimal transport problem. We propose two…

We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost might learn fake plans which are not optimal. To…

We consider the optimal risk sharing problem with a continuum of agents, modeled via a non-atomic measure space. Individual preferences are not assumed to be convex. We show the multiplicity of agents induces the value function to be…

This paper introduces two variational formulations for a model of robust optimal transport, that is, the problem of designing optimal transport networks that are resilient to potential damages, balancing construction costs against the…

Non-negative matrix and tensor factorisations are a classical tool for finding low-dimensional representations of high-dimensional datasets. In applications such as imaging, datasets can be regarded as distributions supported on a space…

Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…

Traditional insurance pricing relies on risk-based principles that ensure actuarial fairness and solvency but do not explicitly account for policyholders' price sensitivity. We formulate insurance pricing as a decision-making problem and…

We investigate the estimation of an optimal transport map between probability measures on an infinite-dimensional space and reveal its minimax optimal rate. Optimal transport theory defines distances within a space of probability measures,…

We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm.…

This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do…

Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…

A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition…

We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…

Here we propose a general theoretical method for analyzing the risk bound in the presence of adversaries. Specifically, we try to fit the adversarial learning problem into the minimax framework. We first show that the original adversarial…

We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over…

We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…

In this note we consider a system of financial institutions and study systemic risk measures in the presence of a financial market and in a robust setting, namely, where no reference probability is assigned. We obtain a dual representation…

We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…

We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of…

We formulate a dynamic reinsurance problem in which the insurer seeks to control the terminal distribution of its surplus while minimizing the L2-norm of the ceded risk. Using techniques from martingale optimal transport, we show that,…