Related papers: Risk measures based on weak optimal transport

In this paper, we refine and generalize closed forms for worst-case law invariant convex risk measures with uncertainty sets based on: i) closed balls under $p$-norms and Wasserstein distance; and ii) moment constraints involving mean and…

Recently, literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. A running example includes Cumulative prospect theory and Conditional variance at risk. Most of them can be can be…

We study a class of dynamically consistent risk measures that robustify a time-homogeneous Markovian reference model by allowing for distributional uncertainty in its transition laws. We start from one-step convex risk evaluations in which…

In this article, we propose a novel characterization of law-invariant and coherent risk measures, based on a generalized optimal transport problem in which the second marginal of the admissible plans is not fixed, but required to lie within…

The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g. in case of fixed transaction costs or when only a finite…

In this paper, we study two classes of optimal reinsurance models from perspectives of both insurers and reinsurers by minimizing their convex combination where the risk is measured by a distortion risk measure and the premium is given by a…

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…

Weak optimal transport generalizes the classical theory of optimal transportation to nonlinear cost functions and covers a range of problems that lie beyond the traditional theory - including entropic transport, martingale transport, and…

We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the…

We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…

We develop a method for computing policies in Markov decision processes with risk-sensitive measures subject to temporal logic constraints. Specifically, we use a particular risk-sensitive measure from cumulative prospect theory, which has…

This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…

De Finetti's optimal reinsurance is a set of contracts, one for each risk in a portfolio, that caps the retained aggregate variance to a pre-specified level while minimizing total expected loss. The premiums are determined using the…

We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a coupling that does not depend on the underlying cost…

In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…

This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…

We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex…

Risk measures connect probability theory or statistics to optimization, particularly to convex optimization. They are nowadays standard in applications of finance and in insurance involving risk aversion. This paper investigates a wide…

We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is…

The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk averse optimization problems. Despite its theoretical appeal, the implementation of a…