Applied Set-Valued Analysis and Optimization

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DOI: 10.23952/asvao.3.2021.3.09
Volume 3, Issue 3, 31 December 2021, Pages 355-380

 

Abstract. In this paper, we study the properties of certain risk measures associated with acceptance sets. These sets describe the regulatory preconditions that have to be fulfilled by financial institutions to pass a given acceptance test. If the financial position of an institution is not acceptable, the decision maker has to raise new capital and invest it into a basket of so called eligible assets to change the current position such that the resulting one corresponds with an element of the acceptance set. Risk measures have been widely studied in the literature. The risk measure that is considered here determines the minimal costs of making a financial position acceptable. In the literature, monetary risk measures are often defined as translation invariant functions and, thus, there is an equivalent formulation as the Gerstewitz-Functional, which is an useful tool for separation and scalarization in multiobjective optimization in the non-convex case. In our paper, we study properties of the sublevel sets, strict sublevel sets, and level lines of a risk measure defined on a linear space. Furthermore, we discuss the finiteness of the risk measure and relax the closedness assumptions.

 

How to Cite this Article:
Marcel Marohn, Christiane Tammer, A new view on risk measures associated with acceptance sets, Appl. Set-Valued Anal. Optim. 3 (2021), 355-380.