Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation

Risk capital allocations (RCAs) are an important tool in quantitative risk management, where they utilized to, e.g., gauge the profitability of distinct business units, determine price a new product, and conduct marginal economic analysis. Nevertheless, notion RCA has been living shadow another, closely related notion, measure (RM) sense that latter often shapes fashion which former is implemented. In fact, as majority RCAs known nowadays induced by RMs, popularity two apparently very much correlated. As result, it Conditional Tail Expectation (CTE) RM arguably prevailed scholarly literature applications. Admittedly, CTE sound mathematical object regulatory RM, but its appropriateness controversial in, analysis pricing. this paper, we address question to whether or not may concur with alternatives arise from context profit maximization. More specifically, provide exhaustive description all those probabilistic model settings, also reflect perception profit-maximizing insurer.