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In this paper we make a short survey on the problem of Capital Allocation through the use of risk measures and we apply some of the most popular Capital Allocation methods to a portfolio of risky positions by using Value at Risk, Conditional Value at Risk and the entropic risk measure. We then discuss and compare the results found in our numerical example.

This paper deals with the problem of capital allocation for a peculiar class of risk measures, namely the Haezendonck-Goovaerts (HG) ones. We generalize the capital allocation rule (CAR) introduced by Xun et al. for Orlicz risk premia, using firstly an approach based on Orlicz quantiles and secondly a more general one based on the, here introduced, concept of linking functions. Further on, we use the same construction of to extend the CARs previously introduced to HG risk measures. We therefore study the properties of different CARs for HG risk measures, both in the quantile-based setting and in the linking one. Finally, we provide robust versions of the introduced CARs, both considering the case of ambiguity over the probabilistic model and the one of multiple Young functions, following the scheme of.

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 the allocation of risk. We define the notion of risk contribution rule and show how in this context it is interpretable as a tool for assessing the contribution of a sub-portfolio to a given portfolio in terms of acceptability without necessarily involving a risk measure. Furthermore, we investigate under which conditions on a risk contribution rule a representation of an acceptance set holds in terms of the risk contribution rule itself, thus extending to this setting the interpretation, classical in risk measures theory, of minimal amount required to hedge a risky position.

This paper makes the point on a well known property of capital allocation rules, namely the one called no-undercut. Its desirability in capital allocation stems from some stability game theoretical features that are related to the notion of core, both for finite and infinite games. We review these aspects, by relating them to the properties of the risk measures that are involved in capital allocation problems. We also discuss some problems and possible extensions that arise when we deal with non-coherent risk measures.