Abstract
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.
Highlights
There is a consistent number of capital allocation methods that correspond to different objectives; one popular approach is based on a set of reasonable axioms, and it is related to cooperative game theory, as, for example, in the works of Denault [14] and Csóka et al [22], while others are mainly based on the evaluation of performance of portfolios/activities, optimization principles, or pricing issues
We have focused on the first streamline initiated by the works of Denault [14] and Kalkbrener [16], by concentrating, in particular, on the study of the property known in the literature as no-undercut
This property entails game theoretical features in that, when satisfied, it guarantees that the allocation to the various sub-portfolios of a portfolio is stable
Summary
In the case of portfolios of financial positions in different currencies that can not be aggregated due to liquidity constraints and/or transaction costs (see [26,27]), it is reasonable to consider risk measures that associate, to any portfolio in different currencies, a set of hedging deterministic positions In this framework, Centrone and Rosazza Gianin [24] defined a set-valued capital allocation rule (with respect to a set-valued risk measure R) as a setvalued map Λ that associates to every X, Y ∈ L∞.
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