Computing risk profiles for composite low-probability high-consequence events

Low-probability high-consequence events play an important role is assessing the risk of catastrophic loss. Their risk profiles, however, can be difficult to obtain. This paper obtains the risk profiles of low-probability high-consequence events where the final consequence results from a number of intermediate events. Called composite events, these events occur, for example, in accidents releasing hazardous material. The structure of composite events is described and risk profile equations developed, both on a per-event and per-annum basis. The many extremely low valued terms, especially in the tail of the risk profile, make calculation nontrivial. Accordingly, algorithms are developed to compute these equations. In addition, formulae for means and variances are obtained, and an illustrative example is provided.