What can we see through the lens of allocation triviality?
Risk capital allocations (RCAs) are an important tool in quantitative risk management, where they are utilized to, e.g., gauge the profitability of dis- tinct business units, determine the price of a new product, and conduct the marginal economic capital analysis. Concurrently, the notion of RCA has been living with another closely related notion, that of risk measures (RM), in the sense that the latter often shapes how the former is implemented. Weighted RMs and their RCAs counterparts are a particularly useful class and their significance have gained traction in recent years. This class contains most of the functionals studied and used today. Often times, however, practitioners argue for and resort to simplistic models; specifically, viewing allocation as a trivial standalone exercise where the unit is financially exclusive from the whole. Trivial allocations are therefore not a desirable approach a prudent risk manager should undertake. Alone, triviality may seem inconsequential, however, used in the right context it can reveal some illuminating implications. In this talk we will survey the class of Weighted RMs and RCAs and discuss the necessary conditions of trivial allocations. The scope will include both proportional and absolute triviality where we will entertain what questions can they answer and what connections can they establish.