Recent developments in set optimization are surveyed and extended including various set
relations as well as fundamental constructions of a convex analysis for set-and vector …

Two approximation algorithms for solving convex vector optimization problems (CVOPs) are
provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously …

We study the risk-aware reinforcement learning (RL) problem in the episodic finite-horizon
Markov decision process with unknown transition and reward functions. In contrast to the risk …

New versions of the set-valued average value at risk for multivariate risks are introduced by
generalizing the well-known certainty equivalent representation to the set-valued case. The …

Equivalent characterizations of multi-portfolio time consistency are deduced for closed
convex and coherent set-valued risk measures on L^p(\varOmega,F,P;R^d) with image …

Set-valued dynamic risk measures are defined on with and with an image space in the
power set of. Primal and dual representations of dynamic risk measures are deduced …

A method for calculating multi-portfolio time consistent multivariate risk measures in discrete
time is presented. Market models for d assets with transaction costs or illiquidity and …

Risk measures for multivariate financial positions are studied in a utility-based framework.
Under a certain incomplete preference relation, shortfall and divergence risk measures are …

In this work, we propose an outer approximation algorithm for solving bounded convex
vector optimization problems (CVOPs). The scalarization model solved iteratively within the …

Inspired by the theory of financial markets with transaction costs, we study a concept of
essential supremum in the framework where a random partial order in R d is lifted to the …