Risk Capital Allocation and Cooperative Pricing of Insurance Liabilities

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To Split or Not to Split: Capital Allocation with Convex Risk Measures (2007, unknown): “The risk measure ρg,a has two well known special cases: • For a = 0 we get the distortion or spectral risk measure (Wang (1996), Acerbi (2002)) ρg(X) = E ( X · g(1 − UX) )”
Weighted Pricing Functionals With Applications to Insurance (2009, methodology): “Indeed, when the distortion function g is differentiable and the cdf FX is continuous, then ¯ [X] E[Xg (F (X))], (2.3)g X which is a representation extensively utilized by Tsanakas and Barnett (2003), Tsanakas and Desli (2003), Tsanakas (2004, 2005), and Tsanakas and Christofides (2006).”
Dynamic capital allocation with distortion risk measures (2004, unknown): “Note that the capital allocation problem can also be viewed as a pricing exercise, where a reinsurer passes on to the cedents the savings from pooling liabilities arising from different contracts (Tsanakas and Barnett, 2002).”
Weighted Risk Capital Allocations (2008, unknown): “For examples of the weighted allocation when w does depend on FY , we refer to, e.g., Tsanakas and Barnett (2003), Tsanakas (2008)where the distorted allocation is studied (see Table 2.1); to Denault (2001), Panjer and Jing (2001) for the TCE allocations (see Table 2.1); to Furman and Landsman…”