Abstract
An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be asymptotically proportional to the corresponding Value-at-Risk (VaR) risk measure. The existing methodology acquired for VaR can therefore be applied to a somewhat less well-studied CTE. In the context of interest, the EVT approach is seemingly well-motivated by modern regulations, which openly strive for the excessive prudence in determining risk capitals.
Highlights
IntroductionThe recent financial instability and, as a result, regulators’ inclination to excessive prudence in determining risk capital requirements have to a certain extent enfeebled VaR’s status
Relation (2.15) agrees with the theorem, which provides the asymptotic expressions for the capital allocations for a multi-line insurance business of d asymptotically dependent risks that belong to Maximum Domain of Attraction (MDA)(Λ)
In this paper we considered the problem of allocating the aggregate risk of a multi-line insurance business consisting of dependent risks to the various sources
Summary
The recent financial instability and, as a result, regulators’ inclination to excessive prudence in determining risk capital requirements have to a certain extent enfeebled VaR’s status In this respect, the so-called tail-based risk measurement has emerged as a natural tool for quantifying insurance risks while emphasizing the adverse effect of low probability but high severity tail events. Determine the overall risk capital requirement for an insurance company, it is of consequent interest to decompose the aforementioned capital into the associated risk sources To this end, the functional Q is naturally generalized beyond the conditional state independence, to a risk capital allocation functional, A, from the space of the Cartesian product of X with itself to [0, ∞], and such that A[Xi, Xi] = Q[Xi], i = 1, .
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