OPTIMAL PAYOFFS FOR DIRECTIONALLY CLOSED ACCEPTANCE SETS.

Acceptance sets are used for modeling regulatory preconditions for financial institutes. In this paper, we consider directionally closed acceptance sets in the linear space of capital positions. Assuming finitely many eligible assets, the decision maker of a financial institution has to decide how to invest into these assets to secure acceptability for the financial position, meaning that the resulting capital position belongs to the acceptance set. We study the risk measure that describes the costs for reaching acceptability in the linear space of capital positions. The aim of our paper is to derive a general characterization of the solution set of the optimal payoff map based on our previously published results concerning the properties of the risk measure. Furthermore, we also give some more details about (weakly) efficient points of the acceptance set. [ABSTRACT FROM AUTHOR]