Optimal Capital Allocation Principles

Abstract

This article develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimization argument, requiring that the weighted sum of measures for the deviations of the business unit's losses from their respective allocated capitals be minimized. The approach is fair insofar as it requires capital to be close to the risk that necessitates holding it. The approach is additionally very flexible in the sense that different forms of the objective function can reflect alternative definitions of corporate risk tolerance. Owing to this flexibility, the general framework reproduces several capital allocation methods that appear in the literature and allows for alternative interpretations and possible extensions.

Asymptotics for risk capital allocations based on Conditional Tail Expectation

“…See Section 6.3 of McNeil et al (2005) for related discussions on this allocation as a consequence of the Euler principle, as well as Dhaene et al (2011) for optimality studies of interest. Although (1.1) is quite elegant and satisfies many desirable properties, its analytic tractability for generally distributed and possibly dependent X 1 , .…”

On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory

“…In fact, we show that for the CEVaR β risk measure the Euler allocation method is the only way to allocate the risk capital. We also discuss the connection between our approach and existing results for capital allocation in similar framework, namely that of [7]. In Section 5, we apply our results to study the capital allocation problem for a particular type of insurance Lévy risk process.…”

“…We ultimately give a definition of what we mean by capital allocation in this context and give an explicit solution for it. We also discuss connections between our approach and existing alternative solutions in the literature such as [7].…”

CMPH: a multivariate phase-type aggregate loss distribution

“…A great variety of capital allocation rules have been proposed in the literature (e.g., Dhaene, Tsanakas, Valdez and Vandu el [8]; Furman and Zitikis [13,14]; and references therein). Before introducing three illustrative examples, which we shall explore numerically in the next section, we rst familiarize with basic notation and terminology.…”