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Risk capital allocations (RCAs) are an important tool in quantitative riskmanagement, where they are utilized to, e.g., gauge the profitability ofdistinct business units, determine the price of a new product, and conduct themarginal economic capital analysis. Nevertheless, the notion of RCA has beenliving in the shadow of another, closely related notion, of risk measure (RM)in the sense that the latter notion often shapes the fashion in which theformer notion is implemented. In fact, as the majority of the RCAs knownnowadays are induced by RMs, the popularity of the two are apparently very muchcorrelated. As a result, it is the RCA that is induced by the Conditional TailExpectation (CTE) RM that has arguably prevailed in scholarly literature andapplications. Admittedly, the CTE RM is a sound mathematical object and animportant regulatory RM, but its appropriateness is controversial in, e.g.,profitability analysis and pricing. In this paper, we address the question asto whether or not the RCA induced by the CTE RM may concur with alternativesthat arise from the context of profit maximization. More specifically, weprovide exhaustive description of all those probabilistic model settings, inwhich the mathematical and regulatory CTE RM may also reflect the riskperception of a profit-maximizing insurer.

Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of Conditional Tail Expectation