Capital Allocation Rules and Acceptance Sets
24 Pages Posted: 18 Mar 2020
Date Written: February 19, 2020
Abstract
This paper introduces a new approach to face capital allocation problems from the perspective of acceptance sets, by defining the family of sub-acceptance sets. We study the relations between the notions of sub-acceptability and acceptability of a risky position as well as their impact on capital allocation rules; in this context, indeed, capital allocation rules are interpretable as tools for assessing the contribution of a sub-portfolio to a given portfolio in terms of acceptability instead of necessarily involving a risk measure. Furthermore, we investigate under which conditions on a capital allocation rule a representation of an acceptance set holds in terms of the capital allocation rule itself, thus extending to this setting the interpretation, classical in risk measures theory, of minimal amount required to hedge a risky position.
Keywords: Capital allocation, acceptance sets, convex risk measures, quasi-convex risk measures
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