Set optimization—a rather short introduction
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 …
relations as well as fundamental constructions of a convex analysis for set-and vector …
Benson type algorithms for linear vector optimization and applications
New versions and extensions of Benson's outer approximation algorithm for solving linear
vector optimization problems are presented. Primal and dual variants are provided in which …
vector optimization problems are presented. Primal and dual variants are provided in which …
Primal and dual approximation algorithms for convex vector optimization problems
Two approximation algorithms for solving convex vector optimization problems (CVOPs) are
provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously …
provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously …
Multivariate risk measures: a constructive approach based on selections
I Molchanov, I Cascos - Mathematical Finance, 2016 - Wiley Online Library
Since risky positions in multivariate portfolios can be offset by various choices of capital
requirements that depend on the exchange rules and related transaction costs, it is natural …
requirements that depend on the exchange rules and related transaction costs, it is natural …
Shortfall Deviation Risk: an alternative to risk measurement
MB Righi, PS Ceretta - arXiv preprint arXiv:1501.02007, 2015 - arxiv.org
We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected
loss that occurs with certain probability penalized by the dispersion of results that are worse …
loss that occurs with certain probability penalized by the dispersion of results that are worse …
Multi-portfolio time consistency for set-valued convex and coherent risk measures
Z Feinstein, B Rudloff - Finance and Stochastics, 2015 - Springer
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 …
convex and coherent set-valued risk measures on L^p(\varOmega,F,P;R^d) with image …
Existence, uniqueness, and stability of optimal payoffs of eligible assets
In a capital adequacy framework, risk measures are used to determine the minimal amount
of capital that a financial institution has to raise and invest in a portfolio of prespecified …
of capital that a financial institution has to raise and invest in a portfolio of prespecified …
A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective
In this work we give a comprehensive overview of the time consistency property of dynamic
risk and performance measures, focusing on a the discrete time setup. The two key …
risk and performance measures, focusing on a the discrete time setup. The two key …
Time consistency of dynamic risk measures in markets with transaction costs
Z Feinstein, B Rudloff - Quantitative Finance, 2013 - Taylor & Francis
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 …
power set of. Primal and dual representations of dynamic risk measures are deduced …
[HTML][HTML] Conditional cores and conditional convex hulls of random sets
E Lépinette, I Molchanov - Journal of Mathematical Analysis and …, 2019 - Elsevier
We define two non-linear operations with random (not necessarily closed) sets in Banach
space: the conditional core and the conditional convex hull. While the first is sublinear, the …
space: the conditional core and the conditional convex hull. While the first is sublinear, the …